N-CSR

UNITED STATES

SECURITIES AND EXCHANGE COMMISSION

Washington, D.C. 20549

FORM N-CSR

CERTIFIED SHAREHOLDER REPORT OF REGISTERED

MANAGEMENT INVESTMENT COMPANIES

Investment Company Act file number: 811-03326

Morgan Stanley U.S. Government Money Market Trust

(Exact name of registrant as specified in charter)

522 Fifth Avenue, New York, New York             10036

(Address of principal executive offices)                    (Zip code)

John H. Gernon

522 Fifth Avenue, New York, New York 10036

(Name and address of agent for service)

Registrant's telephone number, including area code: 212-296-0289

Date of fiscal year end: January 31,

Date of reporting period: January 31, 2020

Item 1 - Report to Shareholders

INVESTMENT MANAGEMENT

Morgan Stanley U.S. Government Money Market Trust

Annual Report

January 31, 2020

Beginning on January 1, 2021, as permitted by regulations adopted by the Securities and Exchange Commission ("SEC"), paper copies of the Fund's Annual and Semi-Annual Reports to Shareholders ("Shareholder Reports") will no longer be sent by mail, unless you specifically request paper copies of the Shareholder Reports from the Fund or from your financial intermediary, such as a broker-dealer or a bank. Instead, the Shareholder Reports will be made available on the Fund's website, https://www.morganstanley.com/im/moneymarketfundsshareholderreports and you will be notified by mail each time a Shareholder Report is posted and provided with a website link to access the Shareholder Report. If you already elected to receive Shareholder Reports electronically, you will not be affected by this change and you need not take any action. You may elect to receive Shareholder Reports and other communications from the Fund electronically anytime by contacting your financial intermediary or, if you are a direct investor, please follow the instructions on the envelope.

Beginning on January 1, 2019, you may elect to receive all future Shareholder Reports in paper free of charge. If you invest through a financial intermediary, you can contact your financial intermediary to request that you continue to receive paper copies of your Shareholder Reports. If you invest directly with the Fund, please follow the instructions on the envelope to let the Fund know you wish to continue receiving paper copies of your Shareholder Reports. Your election to receive Shareholder Reports in paper will apply to all funds held in your account if you invest through your financial intermediary or all funds held with the fund complex if you invest directly with a fund.

Morgan Stanley U.S. Government Money Market Trust

Table of Contents

Welcome Shareholder	3
Fund Report	4
Expense Example	10
Portfolio of Investments	11
Statement of Assets and Liabilities	16
Statement of Operations	17
Statements of Changes in Net Assets	18
Notes to Financial Statements	19
Financial Highlights	27
Report of Independent Registered Public Accounting Firm	29
Privacy Notice	30
Trustee and Officer Information	33

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Welcome Shareholder,

We are pleased to provide this Annual Report, in which you will learn how your investment in Morgan Stanley U.S. Government Money Market Trust (the "Fund") performed during the latest twelve-month period. It includes an overview of the market conditions and discusses some of the factors that affected performance during the reporting period. In addition, the report contains financial statements and a list of portfolio holdings.

Morgan Stanley Investment Management is a client-centric, investor-led organization. Our global presence, intellectual capital, and breadth of products and services enable us to partner with investors to meet the evolving challenges of today's financial markets. We aim to deliver superior investment service and to empower our clients to make the informed decisions that help them reach their investment goals.

As always, we thank you for selecting Morgan Stanley Investment Management and look forward to working with you in the months and years ahead.

This material must be preceded or accompanied by a prospectus for the fund being offered.

Market forecasts provided in this report may not necessarily come to pass. There is no assurance that a mutual fund will achieve its investment objective. You could lose money by investing in the Fund. Although the Fund seeks to preserve the value of your investment at $1.00 per share, it cannot guarantee it will do so. An investment in a money market fund is not insured or guaranteed by the Federal Deposit Insurance Corporation or any other government agency. The Fund's sponsor has no legal obligation to provide financial support to the Fund and you should not expect that the sponsor will provide financial support to the Fund at any time.

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Fund Report (unaudited)

For the year ended January 31, 2020

Market Conditions

During the first quarter of 2019, U.S. gross domestic product (GDP) came in at 3.1 percent (annualized), slightly below market expectations, as net exports and inventories gave a substantial boost to quarterly growth.⁽ⁱ⁾ The pace of non-farm payrolls averaged 139,000 in the first quarter of 2019, down from the 172,000 average pace from the prior quarter.⁽ⁱⁱ⁾ Payrolls in February 2019 were weak and expected to slow post the holiday season, with March 2019 payrolls rebounding. The unemployment rate was 3.8 percent in March 2019 and continued its downward trend.

In his semiannual testimony on the state of monetary policy to Congress in February 2019, Federal Reserve (Fed) Chairman Powell characterized the economy as "strong." In his speech, Chairman Powell stated that "muted" inflation pressures as well as economic and financial crosscurrents were conflicting signals influencing the Federal Open Market Committee (FOMC or the Committee) to take a "patient" approach in delivering policy changes. He maintained the Fed's wait-and-see approach and underscored the need for being data dependent going forward. Chairman Powell noted that risks to global growth posed a key threat to the outlook, especially in Europe and China. In his statement, he commented that "uncertainty is the enemy of business" and that economic activity may have been impacted.

At its March 2019 meeting, the FOMC voted unanimously to maintain the target range for the federal funds rate at 2.25 to 2.50 percent. The FOMC's forward-looking statements were more dovish than anticipated, with the Committee downgrading expectations for the economy, lowering its outlook for policy rates and ending its balance sheet normalization sooner than expected. In its more dovish outlook, the FOMC revised its federal funds projections to zero rate hikes in 2019 (down from the Committee's expectations of two rate hikes during the December 2018 meeting) and only one rate hike in 2020. As a result, the median fed funds rate forecast was lowered to 2.4 percent from 2.9 percent for 2019 and reduced to 2.6 percent from 3.1 percent for 2020. The pace of balance sheet normalization would also be cut in half to $15 billion starting in May and would end altogether in September 2019, earlier than many economists expected. Fed Chairman Powell stated that while the labor market remained strong, growth in economic activity had decelerated in the first quarter of 2019 due to a number of factors, including slowing growth in Europe and China, concerns over tariffs and the effects of global trade tensions. The FOMC noted that in light of global economic and financial developments and muted inflation pressures, the Committee would be patient as it determined the appropriate path of future policy adjustments.

At the conclusion of its May 1, 2019 meeting, as expected, the FOMC kept the range for the federal funds

(i)  Source for GDP data shown in this report: U.S. Bureau of Economic Analysis.

(ii)  Source for employment data shown in this report: U.S. Bureau of Labor Statistics and Bloomberg L.P.

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rate unchanged at 2.25 to 2.50 percent. The FOMC reiterated its intentions to remain "patient" as it decided the path of future policy adjustments. FOMC participants believed the most likely outcome for the U.S. economy would be sustained expansion of economic activity, with strong labor market conditions and inflation nearing its 2 percent target. Regarding economic conditions, Fed Chairman Powell acknowledged that economic growth and job creation since the Fed's prior meeting in March 2019 had been stronger than anticipated. In addition, Chairman Powell highlighted that international risks had moderated since the beginning of 2019, as evidenced by some recent improvement in global economic data, a delayed Brexit and reports of some progress in U.S.-China trade negotiations. While the federal funds rate remained unchanged, the FOMC lowered the interest on excess reserves (IOER) by 0.05 percent to 2.35 percent from 2.40 percent. Chairman Powell noted the decrease in the IOER was a technical adjustment designed to control overnight rates in the fed funds market and should not be viewed as any change to overall monetary policy.

The Trump administration's decision on May 10, 2019 to raise tariffs to 25 percent on $200 billion of Chinese goods and the threat to levy further tariffs on another $300 billion of Chinese goods following the G20 meeting in June 2019 stoked concerns that the U.S.-China trade war could be longer and more pronounced than expected. The Trump administration's decision on May 29, 2019 to threaten Mexico with a 5 percent tariff only exacerbated these concerns and raised the specter of additional U.S. trade wars with other countries.

Fearing continued trade tensions could weaken economic growth, investors fled to U.S. Treasuries in May 2019. The Treasury yield curve flattened significantly, with the 2-, 5- and 10-year yields falling 34 basis points (bps), 37 bps and 38 bps, respectively, throughout the month, and the belly of the curve becoming inverted.⁽ⁱⁱⁱ⁾ As of May 31, 2019, the 10-year Treasury bond was yielding 22 bps less than the 3-month Treasury bill. The 5-year Treasury bond was yielding 43 bps less than the 3-month Treasury bill as of the same date. Given this shift in sentiment, the market was pricing in at least two rate cuts by the Fed by the end of 2019.

At its June 18-19, 2019 meeting, the FOMC kept the range for the federal funds rate unchanged at 2.25 to 2.50 percent. While it kept policy rates unchanged, the FOMC removed the word "patient" in describing its approach to monetary policy and reiterated it remains ready to take appropriate action should economic uncertainties, such as international trade tensions, negatively impact global growth and inflation.

In its June 2019 updated "dot plot," the FOMC showed that 8 out of 17 officials expected lower rates by the end of 2019 — with 7 members anticipating 50 bps of easing. As a result, the average federal funds forecast for 2019 fell to 2.17 percent (down from 2.49 percent during the March 2019 FOMC meeting) while the median remained unchanged at 2.38 percent. Looking ahead, the median federal funds forecast for 2020 was lowered to 2.13 percent (down from 2.63 percent) and the median forecast for 2021 was lowered to 2.38 percent (down from 2.63 percent).

(iii)  Source for Treasury yields data shown in this report: Bloomberg L.P.

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While reconfirming its 2 percent inflation target, the Fed acknowledged a decline in near-term inflation expectations and cut its median Personal Consumption Expenditures (PCE) and core PCE inflation forecasts for 2019 to 1.5 percent and 1.8 percent, respectively. GDP growth projections for 2019 remained unchanged while the unemployment rate was revised lower to 3.6 percent from 3.7 percent.

Second quarter 2019 GDP cooled to 2.0 percent (annualized) as weaknesses were evident. Businesses showed wariness to expand and delayed investment decisions as uncertainties surrounding trade tension mounted. However, personal consumption remained strong and contributed a substantial share of economic growth. The labor market remained strong with the unemployment rate falling to 3.7 percent in June 2019. The pace of non-farm payrolls averaged 159,000 in the second quarter of 2019, up from the first quarter.

Citing weakening global growth and muted inflation pressures, the FOMC lowered the range for the federal funds rate by 0.25 percent to 2.00 to 2.25 percent at its July 2019 meeting. While acknowledging the U.S. economy and labor market remained strong, Fed Chairman Powell highlighted global uncertainties, including weaker growth in the European Union and China as risks to the outlook justifying the rate cut. The FOMC reiterated it would "act as appropriate to sustain the expansion," thus leaving the door open to potential future rate cuts if global economic growth continued to weaken. In addition to lowering the federal funds rate, the FOMC lowered the IOER rate by 0.25 percent to

2.10 percent and ended its balance sheet run-off program two months earlier than expected.

On August 1, 2019, President Trump announced the U.S. would impose a 10 percent tariff on the remaining $300 billion of Chinese imports starting September 1, 2019 after negotiations failed to make progress. China pledged to retaliate. The sharp decline in the value of the Chinese yuan that followed led the Trump administration to formally label China a currency manipulator.

The August 2019 employment data showed weaker-than-expected job gains with downward revisions to prior months, but wage growth was surprisingly stronger than expected. Comments from Fed Chairman Powell reflected the challenges of responding to an economy where the job market and the consumer remained strong but was facing headwinds such as the rising trade tensions compounded by a general slowdown in global growth.

At the September 2019 FOMC meeting, the Committee cut policy rates by 25 bps to 1.75 to 2.00 percent as members "judged that downside risks to the outlook for economic activity had increased since their July meeting, particularly those stemming from trade policy uncertainty and conditions abroad." Separately, September 2019 witnessed a spike in overnight repo funding levels, which is not unusual given seasonal pressures related to corporate tax payments and the end of the quarter. However, a confluence of other factors such as the market absorbing an increased supply of Treasury securities after the recent lifting of the debt ceiling,

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exacerbated by lower bank reserves and tight bank balance sheets, raised the Secured Overnight Financing Rate as high as 5.25 percent. The Federal Reserve intervened with temporary open market operations and normalized the repo market for the remainder of September.

Third quarter 2019 GDP expanded more than expected at a 2.1 percent annualized rate, largely due to strength in the consumer spending sector, the biggest part of the economy. After an upward revision to 208,000 jobs created in September 2019, third quarter 2019 non-farm payrolls averaged 203,000, a promising sign that workers continue to find employment opportunities. The jobless rate unexpectedly dropped 0.2 percent to 3.5 percent in September 2019, the lowest reading since December 1969.

As widely expected, the Fed cut interest rates for the third time in 2019 at its October FOMC meeting. In the prepared statement, the Committee dropped its pledge to "act as appropriate to sustain the expansion," while adding in promises to monitor incoming data as members "assess the appropriate path of the target for the federal funds rate." Changes to the statement suggested that policy makers were comfortable leaving interest rates on hold in the near term, while the market ended the month pricing in less than one additional rate cut over the next year. In addition, on October 11, 2019, the Fed announced that it would begin buying $60 billion of Treasury bills per month to improve its control over monetary policy, with a goal of expanding its balance sheet to $1.7 trillion by year-end 2019. While purely technical in nature, short-end Treasuries rallied on the

back of the news, further flattening the yield curve. At the same time, the Fed also announced that it will "conduct term and overnight repurchase agreement operations at least through January of next year to ensure that the supply of reserves remains ample."

The Fed convened on December 10, 2019 for its last meeting of the calendar year. Chairman Powell and the FOMC voted to keep the federal funds rate unchanged at 1.50 to 1.75 percent. Chairman Powell signaled to the market that the Fed was comfortable with current policy and would take a "wait and see" approach going forward. The Federal Reserve press release stated that the current stance of monetary policy was appropriate to support economic expansion, strong labor markets and inflation near the FOMC's symmetric 2 percent objective. Overall, 2019 was eventful for the Fed and Chairman Powell. Entering 2019, investors expected rates to rise systematically during the year, but received quite the opposite policy action.

For the fourth quarter of 2019, GDP growth came in at 2.1 percent (annualized), slightly above market estimates. Personal spending and business investment were weaker, but GDP growth was aided by the housing market. Non-farm payrolls averaged 197,000 during the fourth quarter with the unemployment rate remaining low at 3.5 percent in December 2019.

On January 28, 2020, the Fed held its first policy meeting of the new decade. Although the federal funds rate was unchanged at 1.50 to 1.75 percent, policy committee members opted to increase the IOER rate by 5 bps to 1.60 percent. The modification was a technical

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adjustment done in part to move the IOER rate closer to middle of the fed funds range from the lower end where it has trended in recent months. While most commentary was left unchanged in the accompanying press release, the Fed downgraded household spending from "strong" to "moderate." Similarly, the press release indicated that inflation needs to "return" to its 2 percent target rather than stay "near" the target, which had been used in previous press releases. Overall, the first meeting of 2020 was benign, as Chairman Powell viewed current policy as "appropriate." He reiterated that without any material change in the data going forward, policy was likely to remain unchanged. The January 2020 Fed statement did not address the emerging coronavirus epidemic, but Chairman Powell discussed the risk to the global economy in his press conference.

Performance Analysis

As of January 31, 2020, Morgan Stanley U.S. Government Money Market Trust had net assets of approximately $854.2 million and an average portfolio maturity of 16 days. For the 12-month period ended January 31, 2020, the Fund's Class R and Class S shares provided a total return of 1.85 percent. For the seven-day period ended January 31, 2020, each of the Fund's Class R and Class S shares provided an effective annualized yield of 1.29 percent and a current yield of 1.28 percent, while the 30-day moving average yield for January for Class R and Class S shares was 1.32 percent. Yield quotations more closely reflect the current earnings of the Fund. Past performance is no guarantee of future results.

During the reporting period, we continued to invest in Treasury and government agency debt while holding a large portion of the Fund in overnight repurchase agreements. We continued to focus on conservative positioning and liquidity while being responsive to dynamic market conditions.

There is no guarantee that any sectors mentioned will continue to perform as discussed herein or that securities in such sectors will be held by the Fund in the future.

PORTFOLIO COMPOSITION as of 01/31/20
Repurchase Agreements	58.0	%
U.S. Agency Securities	31.4
U.S. Treasury Security	10.6
MATURITY SCHEDULE as of 01/31/20
1 - 30 Days	84.3	%
31 - 60 Days	11.3
61 - 90 Days	0.8
91 - 120 Days	1.0
121 + Days	2.6

Subject to change daily. Provided for informational purposes only and should not be deemed as a recommendation to buy or sell the types of securities mentioned above. All percentages for portfolio composition and maturity schedule are stated as a percentage of total investments.

Morgan Stanley is a full-service securities firm engaged in securities trading and brokerage activities, investment banking, research and analysis, financing and financial advisory services.

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Investment Strategy

The Fund has adopted a policy to invest exclusively in obligations issued or guaranteed by the U.S. Government and its agencies and instrumentalities and in repurchase agreements collateralized by such securities in order to qualify as a "government money market fund" under federal regulations. The Fund may also hold cash from time to time. A "government money market fund" is a money market fund that invests at least 99.5 percent of its total assets in cash, securities issued or guaranteed by the United States or certain U.S. government agencies or instrumentalities and/or repurchase agreements that are collateralized fully by the foregoing. A "government money market fund" is exempt from requirements that permit money market funds to impose a "liquidity fee" and/or a "redemption gate" that temporarily restricts redemptions. In selecting investments, Morgan Stanley Investment Management Inc. (the Fund's "Adviser") seeks to maintain the Fund's share price at $1.00. The share price remaining stable at $1.00 means that the Fund would preserve the principal value of your investment.

An investment in the Fund is not insured or guaranteed by the Federal Deposit Insurance Corporation or any other government agency. Although the Fund seeks to preserve the value of your investment at $1.00 per share, it is possible to lose money by investing in the Fund.

For More Information About Portfolio Holdings

Each Morgan Stanley fund provides a complete schedule of portfolio holdings in its Semi-Annual and Annual Reports within 60 days of the end of the fund's second and fourth fiscal quarters. The Semi-Annual Reports and the Annual Reports are filed electronically with the Securities and

Exchange Commission ("SEC") on Form N-CSRS and Form N-CSR, respectively. Morgan Stanley also delivers the Semi-Annual and Annual Reports to fund shareholders and makes these reports available on its public website, www.morganstanley.com/im/moneymarketfundsshareholderreports. Each Morgan Stanley non-money market fund also files a complete schedule of portfolio holdings with the SEC for the fund's first and third fiscal quarters as an attachment to Form N-PORT and monthly holdings for each money market fund on Form N-MFP. Morgan Stanley does not deliver these reports to shareholders, nor are the first and third fiscal quarter reports posted to the Morgan Stanley public website. However, the holdings for each money market fund are posted to the Morgan Stanley public website. You may obtain the Form N-PORT filings (as well as the Form N-CSR, N-CSRS and N-MFP filings) by accessing the SEC's website, http://www.sec.gov. You can also request copies of these materials, upon payment of a duplicating fee, by electronic request at the SEC's e-mail address (publicinfo@sec.gov).

Householding Notice

To reduce printing and mailing costs, the Fund attempts to eliminate duplicate mailings to the same address. The Fund delivers a single copy of certain shareholder documents, including shareholder reports, prospectuses and proxy materials, to investors with the same last name who reside at the same address. Your participation in this program will continue for an unlimited period of time unless you instruct us otherwise. You can request multiple copies of these documents by calling (800) 548-7786, 8:00 a.m. to 6:00 p.m., ET. Once our Customer Service Center has received your instructions, we will begin sending individual copies for each account within 30 days.

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Expense Example (unaudited)

As a shareholder of the Fund, you incur ongoing costs, including advisory fees, administration fees, shareholder services fees and other Fund expenses. This example is intended to help you understand your ongoing costs (in dollars) of investing in the Fund and to compare these costs with the ongoing costs of investing in other mutual funds.

This example is based on an investment of $1,000 invested at the beginning of the period and held for the entire period 08/01/19 – 01/31/20.

Actual Expenses

The first line of the table below provides information about actual account values and actual expenses. You may use the information in this line, together with the amount you invested, to estimate the expenses that you paid over the period. Simply divide your account value by $1,000 (for example, an $8,600 account value divided by $1,000 = 8.6), then multiply the result by the number in the first line under the heading entitled "Expenses Paid During Period" to estimate the expenses you paid on your account during this period.

Hypothetical Example for Comparison Purposes

The second line of the table below provides information about hypothetical expenses based on the Fund's actual expense ratio and an assumed rate of return of 5% per year before expenses, which is not the Fund's actual return. The hypothetical account values and expenses may not be used to estimate the actual ending account balance or expenses you paid for the period. You may use this information to compare the ongoing cost of investing in the Fund and other funds. To do so, compare this 5% hypothetical example with the 5% hypothetical examples that appear in the shareholder reports of the other funds.

Please note that the expenses shown in the table are meant to highlight your ongoing costs only. Therefore, the second line of the table is useful in comparing ongoing costs, and will not help you determine the relative total cost of owning different funds that have transactional costs, such as sales charges (loads) or exchange fees.

	Beginning Account Value		Ending Account Value		Expenses Paid During Period(1)
	08/01/19		01/31/20		08/01/19 – 01/31/20
Class R
Actual (0.79% return)	$	1,000.00	$	1,007.89	$	1.74
Hypothetical (5% annual return before expenses)	$	1,000.00	$	1,023.75	$	1.75
Class S
Actual (0.79% return)	$	1,000.00	$	1,007.89	$	1.74
Hypothetical (5% annual return before expenses)	$	1,000.00	$	1,023.75	$	1.75

  (1)  Expenses are equal to the Fund's annualized expense ratios of 0.34% and 0.34% for Class R and Class S shares, respectively, multiplied by the average account value over the period and multiplied by 186**/365 (to reflect the one-half year period).

  **  Adjusted to reflect non-business days accruals.

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Morgan Stanley U.S. Government Money Market Trust

Portfolio of Investments  nJanuary 31, 2020

PRINCIPAL AMOUNT (000)			ANNUALIZED YIELD ON DATE OF PURCHASE			MATURITY DATE	VALUE
		Repurchase Agreements (56.9%)
$	110,000	ABN Amro Securities LLC, (Interest in $750,000,000 joint repurchase agreement, 1.59% dated 01/31/20 under which ABN Amro Securities LLC, will repurchase the securities provided as collateral for $750,099,375 on 02/03/20. The securities provided as collateral at the end of the period held with BNY Mellon, tri-party agent, were various U.S. Government agency securities and U.S. Government obligations with various maturities to 05/15/60 (a); valued at $772,499,999)		1.59	%	02/03/20	$	110,000,000
	25,000	Bank of Montreal, (dated 11/07/19; proceeds $25,106,215; fully collateralized by various U.S. Government agency securities, 2.51% - 4.39% due 09/01/26 - 04/01/47 and U.S. Government obligation, 0.00% - 2.50% due 02/27/20 - 01/31/27; valued at $25,721,362) (Demand 02/07/2020)		1.61		02/10/20		25,000,000
	115,000	Credit Agricole Corp., (Interest in $1,075,000,000 joint repurchase agreement, 1.59% dated 01/31/20 under which Credit Agricole Corp., will repurchase the securities provided as collateral for $1,075,142,438 on 02/03/20. The securities provided as collateral at the end of the period held with BNY Mellon, triparty agent, were various U.S. Government agency securities with various maturities to 11/20/48 (a); valued at $1,107,250,000)		1.59		02/03/20		115,000,000
	25,000	ING Financial Markets LLC, (dated 11/14/19; proceeds $25,106,694; fully collateralized by various U.S. Government agency securities, 3.00% - 5.00% due 01/01/27 - 09/01/57 (a); valued at $25,750,000)		1.67		02/14/20		25,000,000

See Notes to Financial Statements
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Morgan Stanley U.S. Government Money Market Trust

Portfolio of Investments  nJanuary 31, 2020 continued

PRINCIPAL AMOUNT (000)			ANNUALIZED YIELD ON DATE OF PURCHASE			MATURITY DATE	VALUE
$	25,000	Natixis SA, (Interest in $2,250,000,000 joint repurchase agreement, 1.57% dated 01/31/20 under which Natixis, will repurchase the securities provided as collateral for $2,250,294,375 on 02/03/20. The securities provided as collateral at the end of the period held with BNY Mellon, tri-party agent, were various U.S. Government obligations with various maturities to 11/15/48; valued at $2,295,000,000)		1.57	%	02/03/20	$	25,000,000
	15,000	Norinchukin Bank, (dated 12/19/19; proceeds $15,064,458; fully collateralized by a various U.S. Government obligation securities, 0.03% due 11/15/20; valued at $15,300,071)		1.70		03/19/20		15,000,000
	50,000	RBC Dominion Securities, (dated 01/13/20; proceeds $50,199,694; fully collateralized by various U.S. Government agency securities, 2.50% - 4.00% due 12/20/46 - 08/01/48 (a); valued at $51,500,000) (Demand 02/07/2020)		1.58		04/13/20		50,000,000
	10,000	Royal Bank of Canada, (dated 12/11/19; proceeds $10,024,600; fully collateralized by various U.S. Government agency securities, 3.50% - 4.00% due 08/01/42 - 06/01/51 (a); valued at $10,300,000)		1.64		02/03/20		10,000,000
	111,000	Wells Fargo Securities LLC, (Interest in $1,165,000,000 joint repurchase agreement, 1.59% dated 01/31/20 under which Wells Fargo Securities LLC, will repurchase the securities provided as collateral for $1,165,154,363 on 02/03/20. The securities provided as collateral at the end of the period held with BNY Mellon, tri-party agent, were various U.S. Government agency securities with various maturities to 02/01/50 (a); valued at $1,199,950,001)		1.59		02/03/20		111,000,000
		Total Repurchase Agreements(Cost $486,000,000)						486,000,000

See Notes to Financial Statements
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Morgan Stanley U.S. Government Money Market Trust

Portfolio of Investments  nJanuary 31, 2020 continued

PRINCIPAL AMOUNT (000)			ANNUALIZED YIELD ON DATE OF PURCHASE			DEMAND DATE (b)	MATURITY DATE	VALUE
		U.S. Agency Securities (30.9%)
		Federal Farm Credit Bank
$	3,000			1.58	%	—	07/08/20	$	2,979,590
	2,000	SOFR + 0.19%		1.58	(c)	02/03/20	11/18/21		2,000,000
	5,000	3 Month Treasury Money Market Yield + 0.05%		1.59	(c)	02/03/20	10/21/20		4,999,823
	3,000			1.59		—	05/22/20		2,985,648
	1,000	3 Month Treasury Money Market Yield + 0.065%		1.60	(c)	02/03/20	05/01/20		999,990
	2,000	3 Month USD LIBOR - 0.17%		1.62	(c)	04/27/20	01/27/21		2,000,000
	3,000	1 Month USD LIBOR - 0.01%		1.65	(c)	02/20/20	07/20/20		2,999,894
	1,000	SOFR + 0.08%		1.66	(c)	02/03/20	06/10/21		1,000,000
	6,670	1 Month USD LIBOR + 0.00%		1.66	(c)	02/25/20	06/25/20		6,670,816
	5,000	1 Month USD LIBOR + 0.01%		1.67	(c)	02/28/20	08/28/20		5,000,000
	2,000	3 Month Treasury Money Market Yield + 0.14%		1.68	(c)	02/04/20	09/17/21		1,995,479
	2,000	SOFR + 0.105%		1.69	(c)	02/03/20	01/15/21		2,000,000
	4,000	1 Month USD LIBOR + 0.025%		1.69	(c)	02/25/20	08/25/20		3,999,881
	4,740	1 Month USD LIBOR + 0.05%		1.70	(c)	—	02/21/20		4,740,304
	5,000	1 Month USD LIBOR + 0.00%		1.71	(c)	02/07/20	10/07/20		4,999,325
	5,000	1 Month USD LIBOR + 0.035%		1.72	(c)	02/11/20	02/11/21		5,000,000
	3,000	3 Month USD LIBOR - 0.17%		1.73	(c)	02/09/20	11/09/20		2,998,504
	2,000	1 Month USD LIBOR + 0.085%		1.74	(c)	02/29/20	08/30/21		2,000,000
	5,000	1 Month USD LIBOR + 0.09%		1.74	(c)	02/21/20	04/21/21		4,999,955
	7,000	3 Month USD LIBOR - 0.15%		1.75	(c)	03/18/20	09/18/20		7,000,000
	5,000	1 Month USD LIBOR + 0.08%		1.76	(c)	02/13/20	08/13/21		5,000,000
	15,000	1 Month USD LIBOR + 0.01%		1.79	(c)	03/02/20	07/02/20		15,000,000
	1,900	3 Month Treasury Money Market Yield + 0.26%		1.80	(c)	02/03/20	05/17/21		1,899,877
	5,000	1 Month USD LIBOR + 0.10%		1.80	(c)	02/09/20	09/09/21		5,000,000
	3,000	1 Month USD LIBOR + 0.11%		1.81	(c)	02/09/20	07/09/21		3,000,000
	8,000	1 Month USD LIBOR + 0.10%		1.83	(c)	02/05/20	08/05/21		8,000,000
	6,000	1 Month USD LIBOR + 0.19%		1.84	(c)	02/21/20	12/21/20		6,006,515
		Federal Home Loan Bank
	3,000	1 Month USD LIBOR - 0.065%		1.59	(c)	02/20/20	02/20/20		2,999,993
	5,000	SOFR + 0.02%		1.60	(c)	02/03/20	05/22/20		5,000,000
	7,000	SOFR + 0.025%		1.61	(c)	02/03/20	04/22/20		7,000,000
	3,000	SOFR + 0.03%		1.61	(c)	02/03/20	03/06/20		3,000,000
	20,000			1.61		—	03/06/20		19,971,556

See Notes to Financial Statements
13

Morgan Stanley U.S. Government Money Market Trust

Portfolio of Investments  nJanuary 31, 2020 continued

PRINCIPAL AMOUNT (000)			ANNUALIZED YIELD ON DATE OF PURCHASE			DEMAND DATE (b)	MATURITY DATE	VALUE
$	10,000			1.61	%	—	03/09/20	$	9,984,445
	2,000			1.61		—	06/26/20		1,987,240
	5,000	SOFR + 0.03%		1.61	(c)	02/03/20	07/17/20		5,000,000
	5,000	SOFR + 0.03%		1.61	(c)	02/03/20	08/21/20		5,000,000
	10,000	SOFR + 0.035%		1.62	(c)	02/03/20	06/19/20		10,000,000
	1,000	SOFR + 0.04%		1.62	(c)	02/03/20	02/09/21		1,000,000
	5,000	SOFR + 0.045%		1.63	(c)	02/03/20	08/14/20		5,000,000
	6,000	SOFR + 0.045%		1.63	(c)	02/03/20	09/28/20		6,000,000
	1,500	SOFR + 0.05%		1.63	(c)	02/03/20	01/22/21		1,500,000
	4,000	SOFR + 0.06%		1.64	(c)	02/03/20	05/06/20		4,000,000
	5,000	1 Month USD LIBOR - 0.01%		1.65	(c)	02/28/20	08/28/20		5,000,000
	5,000	1 Month USD LIBOR - 0.01%		1.65	(c)	02/25/20	03/25/20		5,000,000
	5,000	SOFR + 0.075%		1.66	(c)	02/03/20	06/11/21		5,000,000
	2,000	SOFR + 0.105%		1.69	(c)	02/03/20	10/01/20		2,000,000
	2,000	SOFR + 0.11%		1.69	(c)	02/03/20	06/10/20		2,000,000
	20,000	SOFR + 0.13%		1.71	(c)	02/03/20	10/16/20		20,000,000
	5,000	1 Month USD LIBOR + 0.05%		1.71	(c)	02/27/20	03/27/20		5,000,000
	5,000	3 Month USD LIBOR - 0.10%		1.78	(c)	04/09/20	10/09/20		5,000,000
	5,000			1.91		—	03/20/20		4,987,925
	7,000			1.95		—	06/17/20		7,000,000
		Total U.S. Agency Securities(Cost $263,706,760)							263,706,760
		U.S. Treasury Securities (10.4%)
		U.S. Treasury Bills
	3,000	(d)		1.87		—	03/12/20		2,994,221
	5,000	(d)		1.90		—	03/19/20		4,988,312
	5,000	(d)		1.91		—	03/26/20		4,986,567
		U.S. Treasury Notes
	10,000			1.13		—	03/31/20		9,988,140
	2,000	3 Month Treasury Money Market Yield + 0.033%		1.57	(c)	02/03/20	04/30/20		2,000,084
	10,000	3 Month Treasury Money Market Yield + 0.043%		1.58	(c)	02/03/20	07/31/20		10,000,271
	16,000	3 Month Treasury Money Market Yield + 0.045%		1.58	(c)	02/03/20	10/31/20		15,996,465
	16,000	3 Month Treasury Money Market Yield + 0.115%		1.65	(c)	02/03/20	01/31/21		15,995,370
	5,000	3 Month Treasury Money Market Yield + 0.22%		1.76	(c)	02/03/20	07/31/21		4,998,645

See Notes to Financial Statements
14

Morgan Stanley U.S. Government Money Market Trust

Portfolio of Investments  nJanuary 31, 2020 continued

PRINCIPAL AMOUNT (000)			ANNUALIZED YIELD ON DATE OF PURCHASE			DEMAND DATE (b)	MATURITY DATE			VALUE
$	2,000	3 Month Treasury Money Market Yield + 0.30%		1.84	(c)%	02/03/20	10/31/21			$	2,001,377
	10,000			2.63		—	07/31/20				10,048,753
	5,000			3.50		—	05/15/20				5,026,006
		Total U.S. Treasury Securities (Cost $89,024,211)									89,024,211
		Total Investments (Cost $838,730,971) (e)						98.2	%		838,730,971
		Other Assets in Excess of Liabilities						1.8			15,441,168
		Net Assets						100.0	%	$	854,172,139

  LIBOR  London Interbank Offered Rate.

  SOFR  Secured Overnight Financing Rate.

  USD  United States Dollar.

  (a)  Perpetual - One or more securities do not have a predetermined maturity date. Rates for these securities are fixed for a period of time, after which they revert to a floating rate. Interest rates in effect are as of January 31, 2020.

  (b)  Date of next interest rate reset.

  (c)  Floating or variable rate securities: The rates disclosed are as of January 31, 2020. For securities based on a published reference rate and spread, the reference rate and spread are indicated in the description in the Portfolio of Investments. Certain variable rate securities may not be based on a published reference rate and spread but are determined by the issuer or agent and are based on current market conditions. These securities do not indicate a reference rate and spread in their description in the Portfolio of Investments.

  (d)  Rate shown is the yield to maturity at January 31, 2020.

  (e)  The aggregate cost for federal income tax purposes approximates the aggregate cost for book purposes.

See Notes to Financial Statements
15

Morgan Stanley U.S. Government Money Market Trust

Financial Statements

Statement of Assets and Liabilities January 31, 2020

Assets:
Investments in securities, at value (cost $838,730,971, including value of repurchase agreements of $486,000,000)	$	838,730,971
Cash		785,681
Receivable for:
Shares of beneficial interest sold		17,237,132
Interest		734,687
Prepaid expenses and other assets		97,217
Total Assets		857,585,688
Liabilities:
Payable for:
Shares of beneficial interest redeemed		3,023,487
Advisory fee		114,672
Distribution fee		76,448
Trustees' fees		42,738
Administration fee		38,224
Dividends to shareholders		20,902
Transfer and sub transfer agent fees		15,586
Accrued expenses and other payables		81,492
Total Liabilities		3,413,549
Net Assets	$	854,172,139
Composition of Net Assets:
Paid-in-capital	$	854,246,222
Total Accumulated Loss		(74,083	)
Net Assets	$	854,172,139
Class R Shares:
Net Assets	$	656,453,943
Shares Outstanding (unlimited shares authorized, $0.01 par value)		656,530,269
Net Asset Value Per Share	$	1.00
Class S Shares:
Net Assets	$	197,718,196
Shares Outstanding (unlimited shares authorized, $0.01 par value)		197,716,816
Net Asset Value Per Share	$	1.00

See Notes to Financial Statements
16

Morgan Stanley U.S. Government Money Market Trust

Financial Statements continued

Statement of Operations For the year ended January 31, 2020

Net Investment Income:
Interest Income	$	17,557,578
Expenses
Advisory fee (Note 3)		1,220,727
Shareholder services fee (Note 4)		813,818
Administration fee (Note 3)		406,909
Professional fees		122,713
Registration fees		95,532
Transfer and sub transfer agent fees (Note 5)		53,772
Custodian fees (Note 6)		29,232
Shareholder reports and notices		27,282
Trustees' fees and expenses		21,456
Other		22,550
Total Expenses		2,813,991
Net Investment Income		14,743,587
Net Realized Gain		5,050
Net Increase	$	14,748,637

See Notes to Financial Statements
17

Morgan Stanley U.S. Government Money Market Trust

Financial Statements continued

Statements of Changes in Net Assets

	FOR THE YEAR ENDED JANUARY 31, 2020			FOR THE YEAR ENDED JANUARY 31, 2019
Increase (Decrease) in Net Assets:
Operations:
Net investment income	$	14,743,587		$	12,612,660
Net realized gain		5,050			9,022
Net Increase		14,748,637			12,621,682
Dividends and Distributions to Shareholders:
Class R shares		(11,127,185	)		(11,417,129	)
Class S shares		(3,616,402	)		(1,195,531	)
Total Dividends and Distributions to Shareholders		(14,743,587	)		(12,612,660	)
Net increase (decrease) from transactions in shares of beneficial interest		186,112,593			(380,159,775	)
Net Increase (Decrease)		186,117,643			(380,150,753	)
Net Assets:
Beginning of period		668,054,496			1,048,205,249
End of Period	$	854,172,139		$	668,054,496

See Notes to Financial Statements
18

Morgan Stanley U.S. Government Money Market Trust

Notes to Financial Statements  nJanuary 31, 2020

1. Organization and Accounting Policies

Morgan Stanley U.S. Government Money Market Trust (the "Fund") is registered under the Investment Company Act of 1940, as amended (the "Act"), as a diversified, open-end management investment company. The Fund applies investment company accounting and reporting guidance. The Fund's investment objectives are security of principal, high current income and liquidity. The Fund was organized as a Massachusetts business trust on November 18, 1981 and commenced operations on February 17, 1982.

The Fund offers two classes of shares, Class R and Class S Shares. The two classes have the same fees and expenses.

The Securities and Exchange Commission ("SEC") has adopted changes to the rules that govern money market funds. The Fund operates as a "government money market fund," which allows the Fund to continue to seek a stable Net Asset Value ("NAV"). The Fund will also be exempt from the requirements relating to the imposition of liquidity fees and/or redemption gates.

The following is a summary of significant accounting policies:

A. Valuation of Investments — Portfolio securities are valued at amortized cost, which approximates fair value, in accordance with Rule 2a-7 under the Act. The amortized cost of an instrument is determined by valuing it at its original cost and thereafter amortizing any discount or premium from its face value at a constant rate until maturity.

B. Accounting for Investments — Security transactions are accounted for on the trade date (date the order to buy or sell is executed). Realized gains and losses on security transactions are determined by the identified cost method. Discounts are accreted and premiums are amortized over the life of the respective securities and are included in interest income. Interest income is accrued daily as earned.

C. Multiple Class Allocations — Investment income, expenses and realized and unrealized gains and losses are allocated to each class of shares based upon the relative net asset value on the date such items are recognized. Shareholder services fees are charged directly to the respective class.

D. Repurchase Agreements — The Fund invests directly with institutions in repurchase agreements. The Fund's custodian receives the collateral, which is marked-to-market daily to determine that the value of the collateral does not decrease below the repurchase price plus accrued interest as earned. If such a decrease occurs, additional collateral will be requested and, when received, will be added to the account to maintain full collateralization.

19

Morgan Stanley U.S. Government Money Market Trust

Notes to Financial Statements  nJanuary 31, 2020 continued

The Fund may enter into repurchase agreements in which eligible securities are transferred into joint trading accounts maintained by the custodian for investment companies advised by Morgan Stanley Investment Management Inc. (the "Adviser"). The Fund will participate on a pro-rata basis with the other investment companies in its share of the securities transferred under such repurchase agreements and in its share of proceeds from any repurchase or other disposition of such securities.

Repurchase agreements are subject to Master Repurchase Agreements, which are agreements between the Fund and its counterparties that typically include provisions which provide for the net settlement of all transactions and collateral with the Fund, through a single payment, in the event of default or termination. Amounts presented on the Portfolio of Investments and Statement of Assets and Liabilities are not net settlement amounts but gross. As indicated on the Portfolio of Investments, the cash or securities to be repurchased exceeds the repurchase price to be paid under the repurchase agreement reducing the net settlement amount to zero.

E. Dividends and Distributions to Shareholders — Dividends and distributions to shareholders are recorded on the close of each business day. Dividends from net investment income, if any, are declared and paid daily. Net realized capital gains, if any, are distributed at least annually.

F. Use of Estimates — The preparation of financial statements in accordance with generally accepted accounting principles in the United States ("GAAP") requires management to make estimates and assumptions that affect the reported amounts and disclosures. Actual results could differ from those estimates.

G. Indemnifications — The Fund enters into contracts that contain a variety of indemnifications. The Fund's maximum exposure under these arrangements is unknown. However, the Fund has not had prior claims or losses pursuant to these contracts and expects the risk of loss to be remote.

2. Fair Valuation Measurements

Financial Accounting Standards Board ("FASB") Accounting Standards Codification^TM ("ASC") 820, "Fair Value Measurement" ("ASC 820"), defines fair value as the value that the Fund would receive to sell an investment or pay to transfer a liability in a timely transaction with an independent buyer in the principal market, or in the absence of a principal market, the most advantageous market for the investment or liability. ASC 820 establishes a three-tier hierarchy to distinguish between (1) inputs that reflect the assumptions market participants would use in valuing an asset or liability developed based on market data obtained from sources independent of the reporting entity (observable inputs); and (2) inputs that reflect the reporting entity's own assumptions about the assumptions market participants would use in valuing an asset or liability developed based on the best information available in the circumstances

20

Morgan Stanley U.S. Government Money Market Trust

Notes to Financial Statements  nJanuary 31, 2020 continued

(unobservable inputs) and to establish classification of fair value measurements for disclosure purposes. Various inputs are used in determining the value of the Fund's investments. The inputs are summarized in the three broad levels listed below:

•  Level 1 — unadjusted quoted prices in active markets for identical investments

•  Level 2 — other significant observable inputs (including quoted prices for similar investments, interest rates, prepayment speeds, credit risk, etc.)

•  Level 3 — significant unobservable inputs including the Fund's own assumptions in determining the fair value of investments. Factors considered in making this determination may include, but are not limited to, information obtained by contacting the issuer, analysts, or the appropriate stock exchange (for exchange-traded securities), analysis of the issuer's financial statements or other available documents and, if necessary, available information concerning other securities in similar circumstances.

The inputs or methodology used for valuing securities are not necessarily an indication of the risk associated with investing in those securities and the determination of the significance of a particular input to the fair value measurement in its entirety requires judgment and considers factors specific to each security.

The following is a summary of the inputs used to value the Fund's investments as of January 31, 2020:

INVESTMENT TYPE	LEVEL 1 UNADJUSTED QUOTED PRICES		LEVEL 2 OTHER SIGNIFICANT OBSERVABLE INPUTS		LEVEL 3 SIGNIFICANT UNOBSERVABLE INPUTS		TOTAL
Assets:
Repurchase Agreements	$	—	$	486,000,000	$	—	$	486,000,000
U.S. Agency Securities		—		263,706,760		—		263,706,760
U.S. Treasury Securities		—		89,024,211		—		89,024,211
Total Assets	$	—	$	838,730,971	$	—	$	838,730,971

Transfers between investment levels may occur as the markets fluctuate and/or the availability of data used in an investment's valuation changes.

21

Morgan Stanley U.S. Government Money Market Trust

Notes to Financial Statements  nJanuary 31, 2020 continued

3. Advisory/Administration Agreements

Pursuant to an Investment Advisory Agreement with the Adviser, the Fund pays the Adviser an advisory fee, accrued daily and paid monthly, by applying the annual rate of 0.15% to the net assets of the Fund determined as of the close of each business day.

The Adviser also serves as the Administrator to the Fund and provides administrative services pursuant to an Administration Agreement for an annual fee, accrued daily and paid monthly, of 0.05% of the Fund's daily net assets.

Under a Sub-Administration Agreement between the Administrator and State Street Bank and Trust Company ("State Street"), State Street provides certain administrative services to the Fund. For such services, the Administrator pays State Street a portion of the fee the Administrator receives from the Fund.

The Adviser/Administrator has agreed to assume all operating expenses of the Fund and to waive the advisory fee and administration fee, as applicable, to the extent that such expenses and fees excluding certain investment related expenses, taxes, interest and other extraordinary expenses (including litigation), on an annualized basis exceeds 0.75% of the average daily net assets of the Fund. Effective July 1, 2019, the Adviser/Administrator has agreed to assume such expenses and make such waivers of fees, as applicable, to the extent that such expenses and fees on an annualized basis exceeds 0.56%. The fee waivers and/or expense reimbursements will continue for at least one year from the date of the Fund's prospectus or until such time that the Fund's Board of Trustees (the "Trustees") act to discontinue all or a portion of such waivers and/or reimbursements when they deem such action is appropriate. This arrangement had no effect during the most recent reporting period.

4. Shareholder Services Plan

Pursuant to a Shareholder Services Plan (the "Plan"), the Fund may pay Morgan Stanley Distribution, Inc. (the "Distributor"), an affiliate of the Adviser/Administrator, as compensation for the provision of services to shareholders a service fee up to the rate of 0.15% on an annualized basis of the average daily net assets of the Fund for Class R and Class S shares.

Reimbursements for these expenses are made in monthly payments by the Fund to the Distributor, which will in no event exceed an amount equal to a payment at the annual rate of 0.15% of the Fund's average daily net assets during the month. Expenses incurred by the Distributor pursuant to the Plan in any fiscal year will not be reimbursed by the Fund through payments accrued in any subsequent fiscal year. For the year ended January 31, 2020, the distribution fee was accrued at the annual rate of 0.10%.

The Distributor and Adviser/Administrator have agreed to waive all or a portion of the Fund's shareholder services fee, advisory fee and administration fee, respectively, and/or reimburse expenses, to the extent that total expenses exceed total income of the Fund on a daily basis. These fee waivers

22

Morgan Stanley U.S. Government Money Market Trust

Notes to Financial Statements  nJanuary 31, 2020 continued

and/or expense reimbursements will continue for at least one year from the date of the Fund's prospectus or until such time that the Trustees act to discontinue all or a portion of such waivers and/or expense reimbursements when they deem such action is appropriate. This arrangement had no effect during the most recent reporting period.

5. Dividend Disbursing and Transfer Agent

The Fund's dividend disbursing and transfer agent is DST Asset Manager Solutions, Inc. ("DST"). Pursuant to a Transfer Agency Agreement, the Fund pays DST a fee based on the number of classes, accounts and transactions relating to the Fund.

6. Custodian Fees

State Street (the "Custodian") also serves as Custodian for the Fund in accordance with a Custodian Agreement. The Custodian holds cash, securities and other assets of the Fund as required by the Act. Custody fees are payable monthly based on assets held in custody, investment purchases and sales activity and account maintenance fees, plus reimbursement for certain out-of-pocket expenses.

7. Transactions with Affiliates

The Fund is permitted to purchase and sell securities ("cross-trade") from and to other Morgan Stanley funds as well as other funds and client accounts for which the Adviser or an affiliate of the Adviser serves as investment adviser, pursuant to procedures approved by the Trustees in compliance with Rule 17a-7 under the Act (the "Rule"). Each cross-trade is executed at the current market price in compliance with provisions of the Rule. For the year ended January 31, 2020, the Fund did not engage in any cross-trade transactions.

The Fund has an unfunded noncontributory defined benefit pension plan covering certain independent Trustees of the Fund who will have served as independent Trustees for at least five years at the time of retirement. Benefits under this plan are based on factors which include years of service and compensation. The Trustees voted to close the plan to new participants and eliminate the future benefits growth due to increases to compensation after July 31, 2003. Aggregate pension costs for the year ended January 31, 2020, included in "Trustees' fees and expenses" in the Statement of Operations, amounted to $222. At January 31, 2020, the Fund had an accrued pension liability of $42,738, which is reflected as "Trustees' fees" in the Statement of Assets and Liabilities.

The Fund has an unfunded Deferred Compensation Plan (the "Compensation Plan"), which allows each independent Trustee to defer payment of all, or a portion, of the fees he or she receives for serving on the Board of Trustees. Each eligible Trustee generally may elect to have the deferred amounts credited

23

Morgan Stanley U.S. Government Money Market Trust

Notes to Financial Statements  nJanuary 31, 2020 continued

with a return equal to the total return on one or more of the Morgan Stanley funds that are offered as investment options under the Compensation Plan. Appreciation/depreciation and distributions received from these investments are recorded with an offsetting increase/decrease in the deferred compensation obligation and do not affect the NAV of the Fund.

8. Shares of Beneficial Interest

Transactions in shares of beneficial interest, at $1.00 per share, were as follows:

	FOR THE YEAR ENDED JANUARY 31, 2020			FOR THE YEAR ENDED JANUARY 31, 2019
CLASS R SHARES
Shares sold		1,451,847,592			2,205,836,669
Shares issued in reinvestment of dividends		11,127,185			11,417,129
Shares redeemed		(1,326,187,748	)		(2,726,039,723	)
Net increase (decrease) — Class R		136,787,029			(508,785,925	)
CLASS S SHARES
Shares sold		355,721,186			191,397,794
Shares issued in reinvestment of dividends		3,616,402			1,195,531
Shares redeemed		(310,012,024	)		(63,967,175	)
Net increase — Class S		49,325,564			128,626,150
Net increase (decrease) in Fund		186,112,593			(380,159,775	)

9. Federal Income Tax Status

It is the Fund's intention to continue to qualify as a regulated investment company and distribute all of its taxable and tax-exempt income. Accordingly, no provision for federal income taxes is required in the financial statements.

FASB ASC 740-10, "Income Taxes — Overall", sets forth a minimum threshold for financial statement recognition of the benefit of a tax position taken or expected to be taken in a tax return. Management has concluded there are no significant uncertain tax positions that would require recognition in the financial statements. If applicable, the Fund recognizes interest accrued related to unrecognized tax benefits in "Interest Expense" and penalties in "Other Expenses" in the Statement of Operations. The Fund files tax returns with the U.S. Internal Revenue Service, New York and various states. Generally, each of the tax years in the four-year period ended January 31, 2020 remains subject to examination by taxing authorities.

24

Morgan Stanley U.S. Government Money Market Trust

Notes to Financial Statements  nJanuary 31, 2020 continued

The tax character of distributions paid may differ from the character of distributions shown for GAAP purposes due to short-term capital gains being treated as ordinary income for tax purposes. The tax character of distributions paid during fiscal years 2020 and 2019 was as follows:

2020 DISTRIBUTIONS PAID FROM: ORDINARY INCOME		2019 DISTRIBUTIONS PAID FROM: ORDINARY INCOME
$	14,743,587	$	12,612,660

The amount and character of income and gains to be distributed are determined in accordance with income tax regulations which may differ from GAAP. These book/tax differences are either considered temporary or permanent in nature.

Temporary differences are attributable to differing book and tax treatments for the timing of the recognition of gains (losses) on certain investment transactions and the timing of the deductibility of certain expenses.

The Fund had no permanent differences causing reclassifications among the components of net assets for the year ended January 31, 2020.

At January 31, 2020, the components of distributable earnings for the Fund on a tax basis were as follows:

UNDISTRIBUTED ORDINARY INCOME		UNDISTRIBUTED LONG-TERM CAPITAL GAIN
$	14,405		—

10. Risks Relating to Certain Financial Instruments, Market and Geopolitical

The Fund may invest in, or receive as collateral for repurchase agreements, securities issued by Federal National Mortgage Association ("FNMA") and Federal Home Loan Mortgage Corporation ("FHLMC"). Securities issued by FNMA and FHLMC are not backed by or entitled to the full faith and credit of the United States and are supported by the right of the issuer to borrow from the U.S. Department of the Treasury.

The Federal Housing Finance Agency ("FHFA") serves as conservator of FNMA and FHLMC and the U.S. Department of the Treasury has agreed to provide capital as needed to ensure FNMA and FHLMC continue to provide liquidity to the housing and mortgage markets.

The Fund may enter into repurchase agreements under which the Fund sends cash and takes possession of securities with an agreement that the counterparty will repurchase such securities. In the

25

Morgan Stanley U.S. Government Money Market Trust

Notes to Financial Statements  nJanuary 31, 2020 continued

event of default on the obligation to repurchase, the Fund has the right to liquidate the collateral and apply the proceeds in satisfaction of the obligation. In the event of default or bankruptcy by the counterparty to the agreement, realization of the collateral proceeds may be subject to certain costs and delays.

The value of your investment in the Fund is based on the market prices of the securities the Fund holds. These prices change daily due to economic and other events that affect markets generally, as well as those that affect particular regions, countries, industries, companies or governments. These price movements, sometimes called volatility, may be greater or less depending on the types of securities the Fund owns and the markets in which the securities trade. The increasing interconnectivity between global economies and financial markets increases the likelihood that events or conditions in one region or financial market may adversely impact issuers in a different country, region or financial market. Securities in the Fund's portfolio may underperform due to inflation (or expectations for inflation), interest rates, global demand for particular products or resources, natural disasters, pandemics, epidemics, terrorism, regulatory events and governmental or quasi-governmental actions. The occurrence of global events similar to those in recent years, such as terrorist attacks around the world, natural disasters, pandemics, epidemics, social and political discord or debt crises and downgrades, among others, may result in market volatility and may have long term effects on both the U.S. and global financial markets. It is difficult to predict when similar events affecting the U.S. or global financial markets may occur, the effects that such events may have and the duration of those effects. Any such event(s) could have a significant adverse impact on the value and risk profile of the Fund's portfolio. There is a risk that you may lose money by investing in the Fund.

11. Other

At January 31, 2020, the Fund had record owners of 10% or greater. Investment activities of these shareholders could have a material impact on the Fund. The aggregate percentage of such owners was 87.6%.

26

Morgan Stanley U.S. Government Money Market Trust

Financial Highlights

Selected ratios and per share data for a share of beneficial interest outstanding throughout each period:

	FOR THE YEAR ENDED JANUARY 31,
	2020			2019			2018			2017(1)			2016
Class R Shares(2)
Selected Per Share Data:
Net asset value, beginning of period	$	1.00		$	1.00		$	1.00		$	1.00		$	1.00
Net income from investment operations		0.018			0.016			0.005			0.000	(3)		0.000	(3)
Less dividends from net investment income		(0.018	)		(0.016	)		(0.005	)		(0.000	)(3)		(0.000	)(3)
Net asset value, end of period	$	1.00		$	1.00		$	1.00		$	1.00		$	1.00
Total Return		1.85	%		1.61	%		0.53	%		0.02	%		0.01	%
Ratios to Average Net Assets:
Net expenses		0.35	%		0.36	%		0.49	%(4)		0.46	%(4)		0.16	%(4)
Net investment income		1.82	%		1.55	%		0.52	%(4)		0.01	%(4)		0.01	%(4)
Supplemental Data:
Net assets, end of period, in millions	$	656		$	520		$	1,028		$	1,274		$	1,190

  (1)  Reflects prior period custodian out-of-pocket expenses that were reimbursed in September 2016. The amount of the reimbursement was immaterial on a per share basis and did not impact the total return of Class R shares. The annualized expense and net investment income ratios would be unchanged as the reimbursement of custodian fees was offset against expense waivers/reimbursements with no impact to the net expenses or net investment income.

  (2)  Effective June 28, 2016, the original class was re-designated as Class R shares.

  (3)  Amount is less than $0.001.

  (4)  If the Fund had borne all of its expenses that were reimbursed or waived by the Distributor and/or Adviser/Administrator, the annualized expense and net investment income (loss) ratios would have been as follows:

PERIOD ENDED	EXPENSE RATIO			NET INVESTMENT INCOME (LOSS) RATIO
January 31, 2018		0.53	%		0.48	%
January 31, 2017		0.58			(0.11	)
January 31, 2016		0.59			(0.42	)

See Notes to Financial Statements
27

Morgan Stanley U.S. Government Money Market Trust

Financial Highlights continued

	FOR THE YEAR ENDED JANUARY 31,									PERIOD FROM
										JUNE 28, 2016(1) TO
	2020			2019			2018			JANUARY 31, 2017(2)
Class S Shares
Selected Per Share Data:
Net asset value, beginning of period	$	1.00		$	1.00		$	1.00		$	1.00
Net income from investment operations		0.018			0.016			0.005			0.000	(3)
Less dividends from net investment income		(0.018	)		(0.016	)		(0.005	)		(0.000	)(3)
Net asset value, end of period	$	1.00		$	1.00		$	1.00		$	1.00
Total Return		1.85	%		1.61	%		0.53	%		0.01	%(5)
Ratios to Average Net Assets:
Net expenses		0.35	%		0.36	%		0.49	%(4)		0.46	%(4)(6)
Net investment income		1.82	%		1.55	%		0.52	%(4)		0.01	%(4)(6)
Supplemental Data:
Net assets, end of period, in thousands	$	197,718		$	148,391		$	19,765		$	50

  (1)  Commencement of Offering.

  (2)  Reflects prior period custodian out-of-pocket expenses that were reimbursed in September 2016. The amount of the reimbursement was immaterial on a per share basis and did not impact the total return of Class S shares. The annualized expense and net investment income ratios would be unchanged as the reimbursement of custodian fees was offset against expense waivers/reimbursements with no impact to the net expenses or net investment income.

  (3)  Amount is less than $0.001.

  (4)  If the Fund had borne all of its expenses that were reimbursed or waived by the Distributor and/or Adviser/Administrator, the annualized expense and net investment income (loss) ratios would have been as follows:

PERIOD ENDED	EXPENSE RATIO			NET INVESTMENT INCOME (LOSS) RATIO
January 31, 2018		0.53	%		0.48	%
January 31, 2017		0.58			(0.11	)

(5)  Not annualized.

(6)  Annualized.

See Notes to Financial Statements
28

Morgan Stanley U.S. Government Money Market Trust

Report of Independent Registered Public Accounting Firm

To the Shareholders and Board of Trustees of
Morgan Stanley U.S. Government Money Market Trust

Opinion on the Financial Statements

We have audited the accompanying statement of assets and liabilities of Morgan Stanley U.S. Government Money Market Trust (the "Fund"), including the portfolio of investments, as of January 31, 2020, and the related statement of operations for the year then ended, the statements of changes in net assets for each of the two years in the period then ended, the financial highlights for each of the five years in the period then ended and the related notes (collectively referred to as the "financial statements"). In our opinion, the financial statements present fairly, in all material respects, the financial position of the Fund at January 31, 2020, the results of its operations for the year then ended, the changes in its net assets for each of the two years in the period then ended and its financial highlights for each of the five years in the period then ended, in conformity with U.S. generally accepted accounting principles.

Basis for Opinion

These financial statements are the responsibility of the Fund's management. Our responsibility is to express an opinion on the Fund's financial statements based on our audits. We are a public accounting firm registered with the Public Company Accounting Oversight Board (United States) ("PCAOB") and are required to be independent with respect to the Fund in accordance with the U.S. federal securities laws and the applicable rules and regulations of the Securities and Exchange Commission and the PCAOB.

We conducted our audits in accordance with the standards of the PCAOB. Those standards require that we plan and perform the audit to obtain reasonable assurance about whether the financial statements are free of material misstatement, whether due to error or fraud. The Fund is not required to have, nor were we engaged to perform, an audit of the Fund's internal control over financial reporting. As part of our audits, we are required to obtain an understanding of internal control over financial reporting, but not for the purpose of expressing an opinion on the effectiveness of the Fund's internal control over financial reporting. Accordingly, we express no such opinion.

Our audits included performing procedures to assess the risks of material misstatement of the financial statements, whether due to error or fraud, and performing procedures that respond to those risks. Such procedures included examining, on a test basis, evidence regarding the amounts and disclosures in the financial statements. Our procedures included confirmation of securities owned as of January 31, 2020 by correspondence with the custodian and others or by other appropriate auditing procedures where replies from others were not received. Our audits also included evaluating the accounting principles used and significant estimates made by management, as well as evaluating the overall presentation of the financial statements. We believe that our audits provide a reasonable basis for our opinion.

We have served as the auditor of one or more Morgan Stanley investment companies since 2000.

Boston, Massachusetts
March 17, 2020

29

Morgan Stanley U.S. Government Money Market Trust

Privacy Notice (unaudited)  April 2019

FACTS	WHAT DOES MSIM DO WITH YOUR PERSONAL INFORMATION?
Why?	Financial companies choose how they share your personal information. Federal law gives consumers the right to limit some but not all sharing. Federal law also requires us to tell you how we collect, share, and protect your personal information. Please read this notice carefully to understand what we do.
What?	The types of personal information we collect and share depend on the product or service you have with us. This information can include: n Social Security number and income n investment experience and risk tolerance n checking account number and wire transfer instructions
How?	All financial companies need to share customers' personal information to run their everyday business. In the section below, we list the reasons financial companies can share their customers' personal information; the reasons MSIM chooses to share; and whether you can limit this sharing.

Reasons we can share your personal information	Does MSIM share?	Can you limit this sharing?
For our everyday business purposes — such as to process your transactions, maintain your account(s), respond to court orders and legal investigations, or report to credit bureaus	Yes	No
For our marketing purposes — to offer our products and services to you	Yes	No
For joint marketing with other financial companies	No	We don't share
For our affiliates' everyday business purposes — information about your transactions and experiences	Yes	No
For our affiliates' everyday business purposes — information about your creditworthiness	No	We don't share
For our affiliates to market to you	No	We don't share
For non-affiliates to market to you	No	We don't share

Questions?Call toll-free (844) 312-6327 or email: imprivacyinquiries@morganstanley.com

30

Morgan Stanley U.S. Government Money Market Trust

Privacy Notice (unaudited) continued  April 2019

Who we are

Who is providing this notice? Morgan Stanley Investment Management, Inc. and its affiliated registered investment advisers, registered broker-dealers, and registered and unregistered funds ("MSIM")

What we do

How does MSIM protect my personal information?	To protect your personal information from unauthorized access and use, we use security measures that comply with federal law. These measures include computer safeguards and secured files and buildings. We have policies governing the proper handling of customer information by personnel and requiring third parties that provide support to adhere to appropriate security standards with respect to such information.
How does MSIM collect my personal information?	We collect your personal information, for example, when you n open an account or make deposits or withdrawals from your account n buy securities from us or make a wire transfer n give us your contact information We also collect your personal information from others, such as credit bureaus, affiliates, or other companies.
Why can't I limit all sharing?	Federal law gives you the right to limit only n sharing for affiliates' everyday business purposes — information about your creditworthiness n affiliates from using your information to market to you n sharing for non-affiliates to market to you State laws and individual companies may give you additional rights to limit sharing. See below for more on your rights under state law.

31

Morgan Stanley U.S. Government Money Market Trust

Privacy Notice (unaudited) continued  April 2019

Definitions

Affiliates	Companies related by common ownership or control. They can be financial and non-financial companies. n Our affiliates include companies with a Morgan Stanley name and financial companies such as Morgan Stanley Smith Barney LLC and Morgan Stanley & Co.
Non-affiliates	Companies not related by common ownership or control. They can be financial and non-financial companies. n MSIM does not share with non-affiliates so they can market to you.
Joint marketing	A formal agreement between non-affiliated financial companies that together market financial products or services to you. n MSIM doesn't jointly market

Other important information

Vermont: Except as permitted by law, we will not share personal information we collect about Vermont residents with Non-affiliates unless you provide us with your written consent to share such information.

California: Except as permitted by law, we will not share personal information we collect about California residents with Non-affiliates and we will limit sharing such personal information with our Affiliates to comply with California privacy laws that apply to us.

32

Morgan Stanley U.S. Government Money Market Trust

Trustee and Officer Information (unaudited)

Independent Trustees:

Name, Birth Year and Address of Independent Trustee	Position(s) Held with Registrant	Length of Time Served*	Principal Occupation(s) During Past 5 Years and Other Relevant Professional Experience	Number of Funds in Fund Complex Overseen by Independent Trustee**		Other Directorships Held by Independent Trustee***
Frank L. Bowman c/o Perkins Coie LLP Counsel to the Independent Trustees 1155 Avenue of the Americas, 22nd Floor New York, NY 10036 Birth Year 1944	Trustee	Since August 2006	President, Strategic Decisions, LLC (consulting) (since February 2009); Director or Trustee of various Morgan Stanley Funds (since August 2006); Chairperson of the Compliance and Insurance Committee (since October 2015); formerly, Chairperson of the Insurance Sub- Committee of the Compliance and Insurance Committee (2007-2015); served as President and Chief Executive Officer of the Nuclear Energy Institute (policy organization) (February 2005-November 2008); retired as Admiral, U.S. Navy after serving over 38 years on active duty including 8 years as Director of the Naval Nuclear Propulsion Program in the Department of the Navy and the U.S. Department of Energy (1996-2004); served as Chief of Naval Personnel (July 1994-September 1996) and on the Joint Staff as Director of Political Military Affairs (June 1992-July 1994); knighted as Honorary Knight Commander of the Most Excellent Order of the British Empire; awarded the Officier de l'Orde National du Mérite by the French Government; elected to the National Academy of Engineering (2009).		86	Director of Naval and Nuclear Technologies LLP; Director Emeritus of the Armed Services YMCA; Member of the National Security Advisory Council of the Center for U.S. Global Engagement and a member of the CNA Military Advisory Board; Trustee of Fairhaven United Methodist Church; Member of the Board of Advisors of the Dolphin Scholarship Foundation; Director of other various non-profit organizations; formerly, Director of BP p.l.c. (November 2010-May 2019).
Kathleen A. Dennis c/o Perkins Coie LLP Counsel to the Independent Trustees 1155 Avenue of the Americas, 22nd Floor New York, NY 10036 Birth Year 1953	Trustee	Since August 2006	President, Cedarwood Associates (mutual fund and investment management consulting) (since July 2006); Chairperson of the Liquidity and Alternatives Sub-Committee of the Investment Committee (since October 2006) and Director or Trustee of various Morgan Stanley Funds (since August 2006); formerly, Senior Managing Director of Victory Capital Management (1993-2006).		86	Director of various non-profit organizations.

33

Morgan Stanley U.S. Government Money Market Trust

Trustee and Officer Information (unaudited) continued

Name, Birth Year and Address of Independent Trustee	Position(s) Held with Registrant	Length of Time Served*	Principal Occupation(s) During Past 5 Years and Other Relevant Professional Experience	Number of Funds in Fund Complex Overseen by Independent Trustee**		Other Directorships Held by Independent Trustee***
Nancy C. Everett c/o Perkins Coie LLP Counsel to the Independent Trustees 1155 Avenue of the Americas, 22nd Floor New York, NY 10036 Birth Year 1955	Trustee	Since January 2015	Chief Executive Officer, Virginia Commonwealth University Investment Company (since November 2015); Owner, OBIR, LLC (institutional investment management consulting) (since June 2014); formerly, Managing Director, BlackRock, Inc. (February 2011-December 2013); and Chief Executive Officer, General Motors Asset Management (a/k/a Promark Global Advisors, Inc.) (June 2005-May 2010).		87	Formerly, Member of Virginia Commonwealth University School of Business Foundation (2005-2016); Member of Virginia Commonwealth University Board of Visitors (2013-2015); Member of Committee on Directors for Emerging Markets Growth Fund, Inc. (2007-2010); Chairperson of Performance Equity Management, LLC (2006-2010); and Chairperson, GMAM Absolute Return Strategies Fund, LLC (2006-2010).
Jakki L. Haussler c/o Perkins Coie LLP Counsel to the Independent Trustees 1155 Avenue of the Americas, 22nd Floor New York, NY 10036 Birth Year 1957	Trustee	Since January 2015	Chairman, Opus Capital Group (since January 1996); formerly, Chief Executive Officer, Opus Capital Group (1996-2019); Director, Capvest Venture Fund, LP (May 2000-December 2011); Partner, Adena Ventures, LP (July 1999-December 2010); Director, The Victory Funds (February 2005-July 2008).		87	Director of Service Corporation International and Member, Audit Committee and Investment Committee; Director of Cincinnati Bell Inc. and Member, Audit Committee and Governance and Nominating Committee; Director of Northern Kentucky University Foundation and Member, Investment Committee; Member of Chase College of Law Transactional Law Practice Center Board of Advisors; Director of Chase College of Law Board of Visitors; formerly, Member, University of Cincinnati Foundation Investment Committee; Member, Miami University Board of Visitors (2008-2011); Trustee of Victory Funds (2005-2008) and Chairman, Investment Committee (2007-2008); Member, Service Provider Committee (2005-2008) and Director of Best Transport (2006-2019).

34

Morgan Stanley U.S. Government Money Market Trust

Trustee and Officer Information (unaudited) continued

Name, Birth Year and Address of Independent Trustee	Position(s) Held with Registrant	Length of Time Served*	Principal Occupation(s) During Past 5 Years and Other Relevant Professional Experience	Number of Funds in Fund Complex Overseen by Independent Trustee**		Other Directorships Held by Independent Trustee***
Dr. Manuel H. Johnson c/o Johnson Smick International, Inc. 220 I Street, NE — Suite 200 Washington, D.C. 20002 Birth Year 1949	Trustee	Since July 1991	Senior Partner, Johnson Smick International, Inc. (consulting firm); Chairperson of the Investment Committee (since October 2006) and Director or Trustee of various Morgan Stanley Funds (since July 1991); Co-Chairman and a founder of the Group of Seven Council (G7C) (international economic commission); formerly, Chairperson of the Audit Committee (July 1991-September 2006), Vice Chairman of the Board of Governors of the Federal Reserve System and Assistant Secretary of the U.S. Treasury.		86	Director of NVR, Inc. (home construction).
Joseph J. Kearns c/o Perkins Coie LLP Counsel to the Independent Trustees 1155 Avenue of the Americas, 22nd Floor New York, NY 10036 Birth Year 1942	Trustee	Since August 1994	Senior Adviser, Kearns & Associates LLC (investment consulting); Chairperson of the Audit Committee (since October 2006) and Director or Trustee of various Morgan Stanley Funds (since August 1994); Director, Rubicorn Investments (since February 2019); formerly, Deputy Chairperson of the Audit Committee (July 2003-September 2006) and Chairperson of the Audit Committee of various Morgan Stanley Funds (since August 1994); CFO of the J. Paul Getty Trust (1982-1999).		87	Prior to August 10, 2016, Director of Electro Rent Corporation (equipment leasing); Prior to December 31, 2013, Director of The Ford Family Foundation.

35

Morgan Stanley U.S. Government Money Market Trust

Trustee and Officer Information (unaudited) continued

Name, Birth Year and Address of Independent Trustee	Position(s) Held with Registrant	Length of Time Served*	Principal Occupation(s) During Past 5 Years and Other Relevant Professional Experience	Number of Funds in Fund Complex Overseen by Independent Trustee**		Other Directorships Held by Independent Trustee***
Michael F. Klein c/o Perkins Coie LLP Counsel to the Independent Trustees 1155 Avenue of the Americas, 22nd Floor New York, NY 10036 Birth Year 1958	Trustee	Since August 2006	Managing Director, Aetos Alternatives Management, LP (since March 2000); Co-President, Aetos Alternatives Management, LP (since January 2004) and Co-Chief Executive Officer of Aetos Alternatives Management, LP (since August 2013); Chairperson of the Fixed Income Sub-Committee of the Investment Committee (since October 2006) and Director or Trustee of various Morgan Stanley Funds (since August 2006); formerly, Managing Director, Morgan Stanley & Co. Inc. and Morgan Stanley Dean Witter Investment Management and President, various Morgan Stanley Funds (June 1998-March 2000); Principal, Morgan Stanley & Co. Inc. and Morgan Stanley Dean Witter Investment Management (August 1997-December 1999).		86	Director of certain investment funds managed or sponsored by Aetos Alternatives Management, LP; Director of Sanitized AG and Sanitized Marketing AG (specialty chemicals).
Patricia Maleski c/o Perkins Coie LLP Counsel to the Independent Trustees 1155 Avenue of the Americas, 22nd Floor New York, NY 10036 Birth Year 1960	Trustee	Since January 2017	Managing Director, JPMorgan Asset Management (2004-2016); Oversight and Control Head of Fiduciary and Conflicts of Interest Program (2015-2016); Chief Control Officer-Global Asset Management (2013-2015); President, JPMorgan Funds (2010-2013); Chief Administrative Officer (2004-2013); various other positions including Treasurer and Board Liaison (since 2001).		87	None.

36

Morgan Stanley U.S. Government Money Market Trust

Trustee and Officer Information (unaudited) continued

Name, Birth Year and Address of Independent Trustee	Position(s) Held with Registrant	Length of Time Served*	Principal Occupation(s) During Past 5 Years and Other Relevant Professional Experience	Number of Funds in Fund Complex Overseen by Independent Trustee**		Other Directorships Held by Independent Trustee***
Michael E. Nugent 522 Fifth Avenue New York, NY 10036 Birth Year 1936	Chair of the Board and Trustee	Chair of the Boards since July 2006 and Trustee since July 1991	Chair of the Boards of various Morgan Stanley Funds (since July 2006); Chairperson of the Governance Committee (since January 2019) and Director or Trustee of various Morgan Stanley Funds (since July 1991); formerly, Chairperson of each of the Closed-End Fund committee (until December 2019) and the Insurance Committee (until July 2006); General Partner, Triumph Capital, L.P. (private investment partnership) (1988-2013).		86	None.
W. Allen Reed c/o Perkins Coie LLP Counsel to the Independent Trustees 1155 Avenue of the Americas, 22nd Floor New York, NY 10036 Birth Year 1947	Vice Chair of the Board and Trustee	Vice Chair of the Boards since 2020 and Trustee since August 2006	Vice Chair of the Boards of various Morgan Stanley Funds (since January 2019); Chairperson of the Equity Sub-Committee of the Investment Committee (since October 2006) and Director or Trustee of various Morgan Stanley Funds (since August 2006); formerly, President and CEO of General Motors Asset Management; Chairman and Chief Executive Officer of the GM Trust Bank and Corporate Vice President of General Motors Corporation (August 1994-December 2005).		86	Formerly, Director of Legg Mason, Inc. (2006-2019); and Director of the Auburn University Foundation (2010-2015).

  *  This is the earliest date the Trustee began serving the Morgan Stanley Funds. Each Trustee serves an indefinite term, until his or her successor is elected.

  **  The Fund Complex includes (as of December 31, 2019) all open-end and closed-end funds (including all of their portfolios) advised by Morgan Stanley Investment Management Inc. (the "Adviser") and any funds that have an adviser that is an affiliated person of the Adviser (including, but not limited to, Morgan Stanley AIP GP LP).

  ***  This includes any directorships at public companies and registered investment companies held by the Trustee at any time during the past five years.

37

Morgan Stanley U.S. Government Money Market Trust

Trustee and Officer Information (unaudited) continued

Executive Officers:

Name, Birth Year and Address of Executive Officer	Position(s) Held with Registrant	Length of Time Served*	Principal Occupation(s) During Past 5 Years
John H. Gernon 522 Fifth Avenue New York, NY 10036 Birth Year 1963	President and Principal Executive Officer	Since September 2013	President and Principal Executive Officer of the Equity and Fixed Income Funds and the Morgan Stanley AIP Funds (since September 2013) and the Liquidity Funds and various money market funds (since May 2014) in the Fund Complex; Managing Director of the Adviser; Head of Public Markets Product Development (since 2006).
Timothy J. Knierim 522 Fifth Avenue New York, NY 10036 Birth Year 1959	Chief Compliance Officer	Since December 2016	Managing Director of the Adviser and various entities affiliated with the Adviser; Chief Compliance Officer of various Morgan Stanley Funds and the Adviser (since December 2016) and Chief Compliance Officer of Morgan Stanley AIP GP LP (since 2014). Formerly, Managing Director and Deputy Chief Compliance Officer of the Adviser (2014-2016); and formerly, Chief Compliance Officer of Prudential Investment Management, Inc. (2007-2014).
Francis J. Smith 522 Fifth Avenue New York, NY 10036 Birth Year 1965	Treasurer and Principal Financial Officer	Treasurer since July 2003 and Principal Financial Officer since September 2002	Managing Director of the Adviser and various entities affiliated with the Adviser; Treasurer (since July 2003) and Principal Financial Officer of various Morgan Stanley Funds (since September 2002).
Mary E. Mullin 522 Fifth Avenue New York, NY 10036 Birth Year 1967	Secretary	Since June 1999	Managing Director of the Adviser; Secretary of various Morgan Stanley Funds (since June 1999).
Michael J. Key 522 Fifth Avenue New York, NY 10036 Birth Year 1979	Vice President	Since June 2017	Vice President of the Equity and Fixed Income Funds, Liquidity Funds, various money market funds and the Morgan Stanley AIP Funds in the Fund Complex (since June 2017); Executive Director of the Adviser; Head of Product Development for Equity and Fixed Income Funds (since August 2013).

  *  This is the earliest date the officer began serving the Morgan Stanley Funds. Each officer serves a one-year term, until his or her successor is elected and qualifies.

38

Transfer Agent

DST Asset Manager Solutions, Inc.
2000 Crown Colony Drive
Quincy, Massachusetts 02169

Custodian

State Street Bank and Trust Company
One Lincoln Street
Boston, Massachusetts 02111

Independent Registered Public Accounting Firm

Ernst & Young LLP
200 Clarendon Street
Boston, Massachusetts 02116

Legal Counsel

Dechert LLP
1095 Avenue of the Americas
New York, New York 10036

Counsel to the Independent Trustees

Perkins Coie LLP
1155 Avenue of the Americas
New York, New York 10036

Adviser and Administrator

Morgan Stanley Investment Management Inc.

522 Fifth Avenue
New York, New York 10036

This report is submitted for the general information of the shareholders of the Fund. For more detailed information about the Fund, its fees and expenses and other pertinent information, please read its Prospectus. The Fund's Statement of Additional Information contains additional information about the Fund, including its Trustees. It is available, without charge, by calling (800) 548-7786.

This report is not authorized for distribution to prospective investors in the Fund unless preceded or accompanied by an effective Prospectus. Please read the Prospectus carefully before investing.

Morgan Stanley Distribution, Inc., member FINRA.

© 2020 Morgan Stanley

DWGANN
2965636 EXP. 03.31.2021

Item 2. Code of Ethics.

(a)       The registrant has adopted a code of ethics (the "Code of Ethics") that applies to its principal executive officer, principal financial officer, principal accounting officer or controller, or persons performing similar functions, regardless of whether these individuals are employed by the registrant or a third party.

(b)       No information need be disclosed pursuant to this paragraph.

(c)       Not applicable.

(d)       Not applicable.

(e)       Not applicable.

(f)       

(1)       The registrant’s Code of Ethics is attached hereto as Exhibit 13 A.

(2)       Not applicable.

(3)       Not applicable.

Item 3. Audit Committee Financial Expert.

The registrant's Board of Trustees has determined that Joseph J. Kearns, an “independent” Trustee, is an “audit committee financial expert" serving on its audit committee. Under applicable securities laws, a person who is determined to be an audit committee financial expert will not be deemed an "expert" for any purpose, including without limitation for the purposes of Section 11 of the Securities Act of 1933, as a result of being designated or identified as an audit committee financial expert. The designation or identification of a person as an audit committee financial expert does not impose on such person any duties, obligations, or liabilities that are greater than the duties, obligations, and liabilities imposed on such person as a member of the audit committee and Board of Trustees in the absence of such designation or identification.

Item 4. Principal Accountant Fees and Services.

(a)(b)(c)(d) and (g). Based on fees billed for the periods shown:

2020

	Registrant			Covered Entities(1)
Audit Fees	$	34,317			N/A
Non-Audit Fees
Audit-Related Fees	$	—	(2)	$	—	(2)
Tax Fees	$	3,588	(3)	$	535,939	(4)
All Other Fees		—		$	30,000	(5)
Total Non-Audit Fees	$	3,588		$	565,939
Total	$	37,905		$	565,939

2019

	Registrant			Covered Entities(1)
Audit Fees	$	34,317			N/A
Non-Audit Fees
Audit-Related Fees	$	—	(2)	$	—	(2)
Tax Fees	$	3,588	(3)	$	8,773,935	(4)
All Other Fees	$	—		$	18,115	(5)
Total Non-Audit Fees	$	3,588		$	8,792,050
Total	$	37,905		$	8,792,050

N/A- Not applicable, as not required by Item 4.

⁽¹⁾ Covered Entities include the Adviser (excluding sub-advisors) and any entity controlling, controlled by or under common control with the Adviser that provides ongoing services to the Registrant.

⁽²⁾ Audit-Related Fees represent assurance and related services provided that are reasonably related to the performance of the audit of the financial statements of the Covered Entities' and funds advised by the Adviser or its affiliates, specifically data verification and agreed-upon procedures related to asset securitizations and agreed-upon procedures engagements.

⁽³⁾ Tax Fees represent tax compliance, tax planning and tax advice services provided in connection with the preparation and review of the Registrant’s tax returns.

⁽⁴⁾ Tax Fees represent tax compliance, tax planning and tax advice services provided in connection with the review of Covered Entities' tax returns.

⁽⁵⁾ All other fees represent project management for future business applications and

improving business and operational processes.

(e)(1) The audit committee’s pre-approval policies and procedures are as follows:

APPENDIX A

AUDIT COMMITTEE

AUDIT AND NON-AUDIT SERVICES

PRE-APPROVAL POLICY AND PROCEDURES

OF THE

MORGAN STANLEY FUNDS

AS ADOPTED AND AMENDED JULY 23, 2004 AND JUNE 15 AND 16, 2016³

1. Statement of Principles

The Audit Committee of the Board is required to review and, in its sole discretion, pre-approve all Covered Services to be provided by the Independent Auditors to the Fund and Covered Entities in order to assure that services performed by the Independent Auditors do not impair the auditor’s independence from the Fund.

The SEC has issued rules specifying the types of services that an independent auditor may not provide to its audit client, as well as the audit committee’s administration of the engagement of the independent auditor. The SEC’s rules establish two different approaches to pre-approving services, which the SEC considers to be equally valid. Proposed services either: may be pre-approved without consideration of specific case-by-case services by the Audit Committee (“general pre-approval”); or require the specific pre-approval of the Audit Committee or its delegate (“specific pre-approval”). The Audit Committee believes that the combination of these two approaches in this Policy will result in an effective and efficient procedure to pre-approve services performed by the Independent Auditors. As set forth in this Policy, unless a type of service has received general pre-approval, it will require specific pre-approval by the Audit Committee (or by any member of the Audit Committee to which pre-approval authority has been delegated) if it is to be provided by the Independent Auditors. Any proposed services exceeding pre-approved cost levels or budgeted amounts will also require specific pre-approval by the Audit Committee.

The appendices to this Policy describe the Audit, Audit-related, Tax and All Other services that have the general pre-approval of the Audit Committee. The term of any general pre-approval is 12 months from the date of pre-approval, unless the Audit Committee considers and provides a different period and states otherwise. The Audit Committee will annually review and pre-approve the services that may be provided by the Independent Auditors without obtaining specific pre-approval from the Audit Committee. The Audit Committee will add to or subtract from the list of general pre-approved services from time to time, based on subsequent determinations.

The purpose of this Policy is to set forth the policy and procedures by which the Audit Committee intends to fulfill its responsibilities. It does not delegate the Audit Committee’s responsibilities to pre-approve services performed by the Independent Auditors to management.

The Fund’s Independent Auditors have reviewed this Policy and believes that implementation of the Policy will not adversely affect the Independent Auditors’ independence.

_____________________

³        This Audit Committee Audit and Non-Audit Services Pre-Approval Policy and Procedures (the “Policy”), adopted as of the date above, supersedes and replaces all prior versions that may have been adopted from time to time.

2. Delegation

As provided in the Act and the SEC’s rules, the Audit Committee may delegate either type of pre-approval authority to one or more of its members. The member to whom such authority is delegated must report, for informational purposes only, any pre-approval decisions to the Audit Committee at its next scheduled meeting.

3. Audit Services

The annual Audit services engagement terms and fees are subject to the specific pre-approval of the Audit Committee. Audit services include the annual financial statement audit and other procedures required to be performed by the Independent Auditors to be able to form an opinion on the Fund’s financial statements. These other procedures include information systems and procedural reviews and testing performed in order to understand and place reliance on the systems of internal control, and consultations relating to the audit. The Audit Committee will approve, if necessary, any changes in terms, conditions and fees resulting from changes in audit scope, Fund structure or other items.

In addition to the annual Audit services engagement approved by the Audit Committee, the Audit Committee may grant general pre-approval to other Audit services, which are those services that only the Independent Auditors reasonably can provide. Other Audit services may include statutory audits and services associated with SEC registration statements (on Forms N-1A, N-2, N-3, N-4, etc.), periodic reports and other documents filed with the SEC or other documents issued in connection with securities offerings.

The Audit Committee has pre-approved the Audit services in Appendix B.1. All other Audit services not listed in Appendix B.1 must be specifically pre-approved by the Audit Committee (or by any member of the Audit Committee to which pre-approval has been delegated).

4. Audit-related Services

Audit-related services are assurance and related services that are reasonably related to the performance of the audit or review of the Fund’s financial statements and, to the extent they are Covered Services, the Covered Entities or that are traditionally performed by the Independent Auditors. Because the Audit Committee believes that the provision of Audit-related services does not impair the independence of the auditor and is consistent with the SEC’s rules on auditor independence, the Audit Committee may grant general pre-approval to Audit-related services. Audit-related services include, among others, accounting consultations related to accounting, financial reporting or disclosure matters not classified as “Audit services”; assistance with understanding and implementing new accounting and financial reporting guidance from rulemaking authorities; agreed-upon or expanded audit procedures related to accounting and/or billing records required to respond to or comply with financial, accounting or regulatory reporting matters; and assistance with internal control reporting requirements under Forms N-CEN and/or N-CSR.

The Audit Committee has pre-approved the Audit-related services in Appendix B.2. All other Audit-related services not listed in Appendix B.2 must be specifically pre-approved by the Audit Committee (or by any member of the Audit Committee to which pre-approval has been delegated).

5. Tax Services

The Audit Committee believes that the Independent Auditors can provide Tax services to the Fund and, to the extent they are Covered Services, the Covered Entities, such as tax compliance, tax planning and tax advice without impairing the auditor’s independence, and the SEC has stated that the Independent Auditors may provide such services.

Pursuant to the preceding paragraph, the Audit Committee has pre-approved the Tax Services in Appendix B.3. All Tax services in Appendix B.3 must be specifically pre-approved by the Audit Committee (or by any member of the Audit Committee to which pre-approval has been delegated).

6. All Other Services

The Audit Committee believes, based on the SEC’s rules prohibiting the Independent Auditors from providing specific non-audit services, that other types of non-audit services are permitted. Accordingly, the Audit Committee believes it may grant general pre-approval to those permissible non-audit services classified as All Other services that it believes are routine and recurring services, would not impair the independence of the auditor and are consistent with the SEC’s rules on auditor independence.

The Audit Committee has pre-approved the All Other services in Appendix B.4. Permissible All Other services not listed in Appendix B.4 must be specifically pre-approved by the Audit Committee (or by any member of the Audit Committee to which pre-approval has been delegated).

7. Pre-Approval Fee Levels or Budgeted Amounts

Pre-approval fee levels or budgeted amounts for all services to be provided by the Independent Auditors will be established annually by the Audit Committee. Any proposed services exceeding these levels or amounts will require specific pre-approval by the Audit Committee. The Audit Committee is mindful of the overall relationship of fees for audit and non-audit services in determining whether to pre-approve any such services.

8. Procedures

All requests or applications for services to be provided by the Independent Auditors that do not require specific approval by the Audit Committee will be submitted to the Fund’s Principal Financial and Accounting Officer and must include a detailed description of the services to be rendered. The Fund’s Principal Financial and Accounting Officer will determine whether such services are included within the list of services that have received the general pre-approval of the Audit Committee. The Audit Committee will be informed on a timely basis of any such services rendered by the Independent Auditors. Requests or applications to provide services that require specific approval by the Audit Committee or Chairman of the Audit Committee will be submitted to the Audit Committee by the Fund's Principal Financial and Accounting Officer,who, after consultation with the Independent Auditors, will discuss whether, the request or application is consistent with the SEC’s rules on auditor independence.

The Audit Committee has designated the Fund’s Principal Financial and Accounting Officer to monitor the performance of all services provided by the Independent Auditors and to determine whether such services are in compliance with this Policy. The Fund’s Principal Financial and Accounting Officer will report to the Audit Committee on a periodic basis on the results of its monitoring. Both the Fund’s Principal Financial and Accounting Officer and management will immediately report to the chairman of the Audit Committee any breach of this Policy that comes to the attention of the Fund’s Principal Financial and Accounting Officer or any member of management.

9. Additional Requirements

The Audit Committee has determined to take additional measures on an annual basis to meet its responsibility to oversee the work of the Independent Auditors and to assure the auditor’s independence from the Fund, such as reviewing a formal written statement from the Independent Auditors delineating all relationships between the Independent Auditors and the Fund, consistent with the PCAOB’s Ethics and Independence Rule 3526, and discussing with the Independent Auditors its methods and procedures for ensuring independence.

10. Covered Entities

Covered Entities include the Fund’s investment adviser(s) and any entity controlling, controlled by or under common control with the Fund’s investment adviser(s) that provides ongoing services to the Fund(s). Beginning with non-audit service contracts entered into on or after May 6, 2003, the Fund’s audit committee must pre-approve non-audit services provided not only to the Fund but also to the Covered Entities if the engagements relate directly to the operations and financial reporting of the Fund. This list of Covered Entities would include:

Morgan Stanley Funds

Morgan Stanley & Co. LLC

Morgan Stanley Investment Management Inc.

Morgan Stanley Investment Management Limited

Morgan Stanley Investment Management Private Limited

Morgan Stanley Asset & Investment Trust Management Co., Limited

Morgan Stanley Investment Management Company

Morgan Stanley Services Company, Inc.

Morgan Stanley Distribution, Inc.

Morgan Stanley AIP GP LP

Morgan Stanley Alternative Investment Partners LP

Morgan Stanley Smith Barney LLC

Morgan Stanley Capital Management LLC

Morgan Stanley Asia Limited

(e)(2) Beginning with non-audit service contracts entered into on or after May 6, 2003, the audit committee also is required to pre-approve services to Covered Entities to the extent that the services are determined to have a direct impact on the operations or financial reporting of the Registrant. 100% of such services were pre-approved by the audit committee pursuant to the Audit Committee’s pre-approval policies and procedures (attached hereto).

(f) Not applicable.

(g) See table above.

(h) The audit committee of the Board of Trustees has considered whether the provision of services other than audit services performed by the auditors to the Registrant and Covered Entities is compatible with maintaining the auditors' independence in performing audit services.

Item 5. Audit Committee of Listed Registrants.

(a) The registrant has a separately-designated standing audit committee established in accordance with Section 3(a)(58)(A) of the Exchange Act whose members are:

Joseph J. Kearns, Jakki L. Haussler, Michael F. Klein and W. Allen Reed.

(b) Not applicable.

Item 6. Schedule of Investments

(a) Refer to Item 1.

(b) Not applicable.

Item 7. Disclosure of Proxy Voting Policies and Procedures for Closed-End Management Investment Companies.

Applicable only to reports filed by closed-end funds.

Item 8. Portfolio Managers of Closed-End Management Investment Companies

Applicable only to reports filed by closed-end funds.

Item 9. Closed-End Fund Repurchases

Applicable only to reports filed by closed-end funds.

Item 10. Submission of Matters to a Vote of Security Holders

There have been no material changes to the procedures by which shareholders may recommend nominee to the Fund’s Board of Trustees since the Fund last provided disclosure in response to this item.

Item 11. Controls and Procedures

(a) The registrant’s principal executive officer and principal financial officer have concluded that the registrant’s disclosure controls and procedures are sufficient to ensure that information required to be disclosed by the registrant in this Form N-CSR was recorded, processed, summarized and reported within the time periods specified in the Securities and Exchange Commission's rules and forms, based upon such officers' evaluation of these controls and procedures as of a date within 90 days of the filing date of the report.

(b) There were no changes in the registrant's internal control over financial reporting that

occurred during the second fiscal quarter of the period covered by this report that has materially affected, or is reasonably likely to materially affect, the registrant's internal control over financial reporting.

Item 12. Disclosure of Securities Lending Activities for Closed End Management Investment Companies.

Not Applicable

Item 13. Exhibits

a. Code of Ethics — Incorporated by Reference to N-CSR filed on Accession No. 0001104659-20- 030556 on March 9, 2020.

(Hyperlink address: https://www.sec.gov/Archives/edgar/data/836487/000110465920030556/a20- 1800_1ex99dcodeeth.htm )

(b) A separate certification for each principal executive officer and principal financial officer of the registrant are attached hereto as part of EX-99.CERT.

SIGNATURES

Pursuant to the requirements of the Securities Exchange Act of 1934 and the Investment Company Act of 1940, the registrant has duly caused this report to be signed on its behalf by the undersigned, thereunto duly authorized.

Morgan Stanley U.S. Government Money Market Trust

/s/ John H. Gernon

John H. Gernon

Principal Executive Officer

March 17, 2020

Pursuant to the requirements of the Securities Exchange Act of 1934 and the Investment Company Act of 1940, this report has been signed by the following persons on behalf of the registrant and in the capacities and on the dates indicated.

/s/ John H. Gernon

John H. Gernon

Principal Executive Officer

March 17, 2020

/s/ Francis Smith

Francis Smith

Principal Financial Officer

March 17, 2020

EX-99.CERT

EXHIBIT 13 B1

CERTIFICATION OF PRINCIPAL EXECUTIVE OFFICER

CERTIFICATIONS

I, John H. Gernon, certify that:

1. I have reviewed this report on Form N-CSR of Morgan Stanley U.S. Government Money Market Trust;

2. Based on my knowledge, this report does not contain any untrue statement of a material fact or omit to state a material fact necessary to make the statements made, in light of the circumstances under which such statements were made, not misleading with respect to the period covered by this report;

3. Based on my knowledge, the financial statements and other financial information included in this report, fairly present in all material respects the financial condition, results of operations, changes in net assets, and cash flows (if the financial statements are required to include a statement of cash flows) of the registrant as of, and for, the periods presented in this report;

4. The registrant’s other certifying officers and I are responsible for establishing and maintaining disclosure controls and procedures (as defined in Rule 30a-3(c) under the Investment Company Act of 1940) and internal control over financial reporting (as defined in Rule 30a-3(d) under the Investment Company Act of 1940) for the registrant and have:

a) designed such disclosure controls and procedures, or caused such disclosure controls and procedures to be designed under our supervision, to ensure that material information relating to the registrant, including its consolidated subsidiaries, is made known to us by others within those entities, particularly during the period in which this report is being prepared;

b) designed such internal control over financial reporting, or caused such internal control over financial reporting to be designed under our supervision, to provide reasonable assurance regarding the reliability of financial reporting and the preparation of financial statements for external purposes in accordance with generally accepted accounting principles;

c) evaluated the effectiveness of the registrant’s disclosure controls and procedures and presented in this report our conclusions about the effectiveness of the disclosure controls and procedures, as of a date within 90 days prior to the filing date of this report based on such evaluation; and

d) disclosed in this report any change in the registrant’s internal control over financial reporting that occurred during the second fiscal quarter of the period covered by this report that has materially affected, or is reasonably likely to materially affect, the registrant’s internal control over financial reporting; and

5. The registrant’s other certifying officer(s) and I have disclosed to the registrant’s auditors and the audit committee of the registrant’s board of trustees (or persons performing the equivalent functions):

a) all significant deficiencies and material weaknesses in the design or operation of internal control over financial reporting which are reasonably likely to adversely affect the registrant’s ability to record, process, summarize, and report financial information; and

b) any fraud, whether or not material, that involves management or other employees who have a significant role in the registrant’s internal controls over financial reporting.

Date: March 17, 2020
	/s/ John H. Gernon
	John H. Gernon
	Principal Executive Officer

EXHIBIT 13 B2

CERTIFICATION OF PRINCIPAL FINANCIAL OFFICER

CERTIFICATIONS

I, Francis Smith, certify that:

1. I have reviewed this report on Form N-CSR of Morgan Stanley U.S. Government Money Market Trust;

2. Based on my knowledge, this report does not contain any untrue statement of a material fact or omit to state a material fact necessary to make the statements made, in light of the circumstances under which such statements were made, not misleading with respect to the period covered by this report;

3. Based on my knowledge, the financial statements and other financial information included in this report, fairly present in all material respects the financial condition, results of operations, changes in net assets, and cash flows (if the financial statements are required to include a statement of cash flows) of the registrant as of, and for, the periods presented in this report;

4. The registrant’s other certifying officers and I are responsible for establishing and maintaining disclosure controls and procedures (as defined in Rule 30a-3(c) under the Investment Company Act of 1940) and internal control over financial reporting (as defined in Rule 30a-3(d) under the Investment Company Act of 1940) for the registrant and have:

a) designed such disclosure controls and procedures, or caused such disclosure controls and procedures to be designed under our supervision, to ensure that material information relating to the registrant, including its consolidated subsidiaries, is made known to us by others within those entities, particularly during the period in which this report is being prepared;

b) designed such internal control over financial reporting, or caused such internal control over financial reporting to be designed under our supervision, to provide reasonable assurance regarding the reliability of financial reporting and the preparation of financial statements for external purposes in accordance with generally accepted accounting principles;

c) evaluated the effectiveness of the registrant’s disclosure controls and procedures and presented in this report our conclusions about the effectiveness of the disclosure controls and procedures, as of a date within 90 days prior to the filing date of this report based on such evaluation; and

d) disclosed in this report any change in the registrant’s internal control over financial reporting that occurred during the second fiscal quarter of the period covered by this report that has materially affected, or is reasonably likely to materially affect, the registrant’s internal control over financial reporting; and

5. The registrant’s other certifying officer(s) and I have disclosed to the registrant’s auditors and the audit committee of the registrant’s board of trustees (or persons performing the equivalent functions):

a) all significant deficiencies and material weaknesses in the design or operation of internal control over financial reporting which are reasonably likely to adversely affect the registrant’s ability to record, process, summarize, and report financial information; and

b) any fraud, whether or not material, that involves management or other employees who have a significant role in the registrant’s internal controls over financial reporting.

Date: March 17, 2020

/s/ Francis Smith

Francis Smith

Principal Financial Officer

EX-99.906CERT

SECTION 906 CERTIFICATION

Certification Pursuant to 18 U.S.C. Section 1350,

As Adopted Pursuant to

Section 906 of the Sarbanes-Oxley Act of 2002

Morgan Stanley U.S. Government Money Market Trust

In connection with the Report on Form N-CSR (the “Report”) of the above-named issuer for the period ended January 31, 2020 that is accompanied by this certification, the undersigned hereby certifies that:

1. The Report fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934; and

2. The information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Issuer.

Date: March 17, 2020	/s/ John H. Gernon
	John H. Gernon
	Principal Executive Officer

SECTION 906 CERTIFICATION

Certification Pursuant to 18 U.S.C. Section 1350,

As Adopted Pursuant to

Section 906 of the Sarbanes-Oxley Act of 2002

Morgan Stanley U.S. Government Money Market Trust

In connection with the Report on Form N-CSR (the “Report”) of the above-named issuer for the period ended January 31, 2020 that is accompanied by this certification, the undersigned hereby certifies that:

1. The Report fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934; and

2. The information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Issuer.

Date: March 17, 2020	/s/ Francis Smith
	Francis Smith
	Principal Financial Officer