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)
Randy Takian 522 Fifth Avenue, New York, New York 10036
(Name and address of agent for service)
Registrant’s telephone number, including area code:				212-296-6990
Date of fiscal year end:	January 31, 2009
Date of reporting period:		January 31, 2009

Item 1 - Report to Shareholders

INVESTMENT MANAGEMENT

Welcome, Shareholder:

In this report, you'll learn about how your investment in Morgan Stanley U.S. Government Money Market Trust performed during the annual period. We will provide an overview of the market conditions, and discuss some of the factors that affected performance during the reporting period. In addition, this report includes the Fund's financial statements and a list of Fund investments.

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. An investment in a money market 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 an investment at $1.00 per share, it is possible to lose money by investing in the fund. Please see the prospectus for more complete information on investment risks.

Fund Report

For the year ended January 31, 2009

Market Conditions

The U.S. economy weakened considerably during the 12-month review period. After rising in the first two quarters of 2008, gross domestic product (GDP) growth fell to –0.5 percent in the third quarter and –3.8 percent in the fourth quarter. Other economic data was even more dispiriting, with employment figures negative for every month of 2008 and consumer confidence falling to levels not seen in decades. In January 2009, the unemployment rate rose to 7.6 percent as non-farm payrolls fell by 598,000, the largest monthly decline in 34 years. The residential housing market remained depressed, as home sales and prices continued to decline. These factors led to increasing concerns about a recession despite a decline in commodity and fuel prices that began in July. By year end, it was confirmed that the economy had, in fact, been in recession since December 2007.

The weakening economic outlook, coupled with credit and liquidity constraints and mortgage defaults, made for an extremely volatile market throughout the period under review. The Federal Reserve (the "Fed") and the Treasury made considerable efforts to support both the market and the economy, including a range of innovative programs as well as aggressive reductions in the federal funds target rate and discount rate. These actions were often taken in coordination with central banks across the developed world. At the end of the period, these measures had in part helped to reduce the credit bellwether London Interbank Offered Rate (LIBOR) from its prior record levels, though LIBOR still remained well above the Fed's policy target range for federal funds of 0.0 percent to 0.25 percent.

Performance Analysis

As of January 31, 2009, Morgan Stanley U.S. Government Money Market Trust had net assets of approximately $1.65 billion and an average portfolio maturity of 34 days. For the 12-month period ended January 31, 2009, the Fund provided a total return of 1.54 percent. For the seven-day period ended January 31, 2009, the Fund provided an effective annualized yield of 0.04 percent and a current yield of 0.04 percent, while its 30-day moving average yield for January was 0.04 percent. Yield quotations more closely reflect the current earnings of the Fund. Past performance is no guarantee of future results.

Our strategy in managing the Fund remained consistent with its long-term focus on maintaining preservation of capital and liquidity. Although the aggressive rate reductions by the Fed drastically lowered short-term yields, the turmoil and uncertainty in the markets remained in force and indeed worsened over the course of the period. As a result, we concentrated the portfolio on assets with shorter maturities. We will continue to focus closely on this strategy in an effort to maximize liquidity for the Fund and its shareholders.

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.

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PORTFOLIO COMPOSITION as of 01/31/09
Repurchase Agreements	39.0	%
US Government Agencies — Discount Notes	25.4
US Government Agencies — Floating Rate Notes	24.5
US Government Agencies — Debenture Bonds	11.1
MATURITY SCHEDULE as of 01/31/09
1 - 30 Days	82.5	%
31 - 60 Days	6.3
61 - 90 Days	0.6
91 - 120 Days	1.9
121 + Days	8.7

Subject to change daily. Provided for informational purposes only and should not be deemed as a recommendation to buy or sell the securities mentioned above. Portfolio composition and maturity schedule are 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.

Investment Strategy

The Fund will invest in high quality, short-term U.S. government securities. The Fund's "Investment Adviser," Morgan Stanley Investment Advisors Inc., 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 semiannual and annual reports within 60 days of the end of the fund's second and fourth fiscal quarters. The semiannual 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 semiannual and annual reports to fund shareholders and makes these reports available on its public web site, www.morganstanley.com. Each Morgan Stanley fund also files a complete schedule of portfolio holdings with the SEC for the fund's first and third fiscal quarters on Form N-Q. Morgan Stanley does not deliver the reports for the first and third fiscal quarters to shareholders, nor are the reports posted to the Morgan Stanley public web site. You may, however, obtain the Form N-Q filings (as well as the Form N-CSR and N-CSRS filings) by accessing the SEC's web site, http://www.sec.gov. You may also review and copy them at the SEC's public reference room in Washington, DC.

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Information on the operation of the SEC's public reference room may be obtained by calling the SEC at (800) SEC-0330. 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) or by writing the public reference section of the SEC, Washington, DC 20549-0102.

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) 869-NEWS, 8:00 a.m. to 8:00 p.m., ET. Once our Customer Service Center has received your instructions, we will begin sending individual copies for each account within 30 days.

4

Expense Example

As a shareholder of the Fund, you incur ongoing costs, including advisory fees; distribution and shareholder servicing; 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.

The example is based on an investment of $1,000 invested at the beginning of the period and held for the entire period 08/01/08 – 01/31/09.

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), and redemption fees, or exchange fees.

	Beginning Account Value		Ending Account Value		Expenses Paid During Period@
	08/01/08		01/31/09		08/01/08 – 01/31/09
Actual (0.47% return)	$	1,000.00	$	1,004.70	$	2.91
Hypothetical (5% annual return before expenses)	$	1,000.00	$	1,022.10	$	2.93

@  Expenses are equal to the Fund's annualized expense ratio of 0.58% multiplied by the average account value over the period, multiplied by 183/366 (to reflect the one-half year period). If the Fund had borne all of its expenses, the annualized expense ratio would have been 0.61%. These figures reflect fees paid in connection with the U.S. Treasury Guarantee Program for Money Market Funds. This fee had an effect of 0.03%.

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Morgan Stanley U.S. Government Money Market Trust

Portfolio of Investments  nJanuary 31, 2009

PRINCIPAL AMOUNT IN THOUSANDS		DESCRIPTION	ANNUALIZED YIELD ON DATE OF PURCHASE			MATURITY DATE	VALUE
		U.S. Government Agencies - Discount Notes (24.6%)
$	390,750	Federal Home Loan Bank		0.01 - 0.74	%	02/02/09 - 12/14/09	$	390,474,093
	14,045	Federal National Mortgage Assoc.		0.53 - 0.66		06/30/09 - 09/15/09		13,991,869
		Total U.S. Government Agencies - Discount Notes (Cost $404,465,962)						404,465,962
		U.S. Government Agencies - Floating Rate Notes (23.6%)
	53,000	Federal Farm Credit Bank		0.31 - 1.31	(a)	02/02/09 - 03/25/09(b)		52,997,013
	239,000	Federal Home Loan Bank		0.25 - 2.22	(a)	02/02/09 - 03/30/09(b)		238,993,229
	97,000	Federal Home Loan Mortgage Corp.		0.22 - 0.35	(a)	02/09/09 - 03/02/09(b)		97,000,439
		Total U.S. Government Agencies - Floating Rate Notes (Cost $388,990,681)						388,990,681
		U.S. Government Agencies - Debenture Bonds (10.7%)
	139,605	Federal Home Loan Banks		0.30 - 2.88		02/06/09 - 12/11/09		140,484,583
	34,321	Federal Home Loan Mortgage Corp.		0.65 - 1.23		09/15/09 - 12/23/09		35,007,576
	1,333	Federal National Mortgage Assoc.		1.22		12/15/09		1,372,159
		Total U.S. Government Agencies - Debenture Bonds (Cost $176,864,318)						176,864,318
		Repurchase Agreements (37.7%)
	86,000	Bank of America (dated 01/30/09; proceeds $86,001,792; fully collateralized by Federal National Mortgage Assoc. 2.50% due 04/09/10 valued at $87,720,731) (Cost $86,000,000)		0.25		02/02/09		86,000,000
	200,000	Barclays Capital LLC (dated 01/30/09; proceeds $200,004,667; fully collateralized by Federal National Mortgage Assoc. 4.50% - 5.50% due 03/01/20 - 05/01/36 and Government National Mortgage Assoc. 6.50% due 07/20/38 valued at $206,000,000) (Cost $200,000,000)		0.28		02/02/09		200,000,000

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

Portfolio of Investments  nJanuary 31, 2009 continued

PRINCIPAL AMOUNT IN THOUSANDS		DESCRIPTION	ANNUALIZED YIELD ON DATE OF PURCHASE			MATURITY DATE			VALUE
$	175,000	BNP Paribas Securities Corp. (dated 01/30/09; proceeds $175,004,375; fully collateralized by Federal National Mortgage Assoc. 4.714% - 5.904% due 11/01/36 and Federal Home Loan Mortgage Corp. 5.175% - 6.768% due 11/01/35 - 12/01/38 valued at $180,250,001) (Cost $175,000,000)		0.30	%	02/02/09			$	175,000,000
	160,000	Goldman Sachs Group, Inc. (dated 01/30/09; proceeds $160,003,867; fully collateralized by Federal National Mortgage Assoc. 5.50% due 09/01/23 - 03/01/38 valued at $164,800,001) (Cost $160,000,000)		0.29		02/02/09				160,000,000
		Total Repurchase Agreements (Cost $621,000,000)								621,000,000
		Total Investments (Cost $1,591,320,961) (c)					96.6	%		1,591,320,961
		Other Assets in Excess of Liabilities					3.4			55,500,128
		Net Assets					100.0	%	$	1,646,821,089

  (a)  Rates shown are rates in effect at January 31, 2009.

  (b)  Date of next interest rate reset.

  (c)  Cost is the same for federal income tax purposes.

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

Financial Statements

Statement of Assets and Liabilities

January 31, 2009

Assets:
Investments in securities, at value (cost $1,591,320,961, including repurchase agreements of $621,000,000)	$	1,591,320,961
Cash		163,105
Receivable for:
Shares of beneficial interest sold		57,690,901
Interest		2,086,736
Prepaid expenses and other assets		217,428
Total Assets		1,651,479,131
Liabilities:
Payable for:
Shares of beneficial interest redeemed		3,955,461
Investment advisory fee		434,888
Administration fee		68,162
Transfer agent fee		51,668
Accrued expenses and other payables		147,863
Total Liabilities		4,658,042
Net Assets	$	1,646,821,089
Composition of Net Assets:
Paid-in-capital	$	1,646,723,153
Accumulated undistributed net investment income		99,410
Distributions in excess of net realized gain		(1,474	)
Net Assets	$	1,646,821,089
Net Asset Value Per Share 1,646,788,065 shares outstanding (unlimited shares authorized of $.01 par value)	$	1.00

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

Financial Statements continued

Statement of Operations

For the year ended January 31, 2009

Net Investment Income:
Interest Income	$	27,998,100
Expenses
Investment advisory fee		5,208,540
Shareholder servicing fee		1,415,325
Transfer agent fees and expenses		758,951
Administration fee		707,663
Mutual fund insurance (Note 11)		226,991
Registration fees		166,703
Shareholder reports and notices		137,037
Professional fees		83,356
Custodian fees		55,735
Trustees' fees and expenses		25,177
Other		64,331
Total Expenses		8,849,809
Less: amounts waived		(206,626	)
Less: expense offset		(21,804	)
Net Expenses		8,621,379
Net Investment Income		19,376,721
Net Realized Gain		32,972
Net Increase	$	19,409,693

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

Financial Statements continued

Statements of Changes in Net Assets

	FOR THE YEAR ENDED JANUARY 31, 2009			FOR THE YEAR ENDED JANUARY 31, 2008
Increase (Decrease) in Net Assets: Operations:
Net investment income	$	19,376,721		$	33,862,226
Net realized gain		32,972			11,894
Net Increase		19,409,693			33,874,120
Dividends and Distributions to Shareholders from:
Net investment income		(19,344,981	)		(33,880,542	)
Net realized gain		(31,688	)		(11,894	)
Total Dividends and Distributions		(19,376,669	)		(33,892,436	)
Net increase from transactions in shares of beneficial interest		726,951,166			140,567,525
Net Increase		726,984,190			140,549,209
Net Assets:
Beginning of period		919,836,899			779,287,690
End of Period (Including accumulated undistributed net investment income of $99,410 and $64,912, respectively)	$	1,646,821,089		$	919,836,899

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

Notes to Financial Statements  nJanuary 31, 2009

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'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 following is a summary of significant accounting policies:

A. Valuation of Investments — Portfolio securities are valued at amortized cost, which approximates market value, in accordance with Rule 2a-7 under the Act .

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.

C. Repurchase Agreements — The Fund may invest 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. If such a decrease occurs, additional collateral will be requested and, when received, will be added to the account to maintain full collateralization.

D. Federal Income Tax Policy — It is the Fund's policy to comply with the requirements of Subchapter M of the Internal Revenue Code applicable to regulated investment companies and to distribute substantially all of its taxable and nontaxable income to its shareholders. Therefore, no provision for federal income tax is required. The Fund files tax returns with the U.S. Internal Revenue Service, New York State and New York City. The Fund follows the provisions of the Financial Accounting Standards Board ("FASB") Interpretation No. 48 ("FIN 48") Accounting for Uncertainty in Income Taxes. FIN 48 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. There are no unrecognized tax benefits in the accompanying 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. Each of the tax years in the four year period January 31, 2009, remains subject to examination by taxing authorities.

E. Dividends and Distributions to Shareholders — The Fund records dividends and distributions to shareholders as of the close of each business day.

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Morgan Stanley U.S. Government Money Market Trust

Notes to Financial Statements  nJanuary 31, 2009 continued

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

2. Investment Advisory/Administration Agreements

Pursuant to an Investment Advisory Agreement with Morgan Stanley Investment Advisors Inc. (the "Investment Adviser"), the Fund pays the Investment Adviser an advisory fee, accrued daily and payable monthly, by applying the following annual rates to the net assets of the Fund determined as of the close of each business day: 0.45% to the portion of the daily net assets not exceeding $500 million; 0.375% to the portion of the daily net assets exceeding $500 million but not exceeding $750 million; 0.325% to the portion of the daily net assets exceeding $750 million but not exceeding $1 billion; 0.30% to the portion of the daily net assets exceeding $1 billion but not exceeding $1.5 billion; 0.275% to the portion of the daily net assets exceeding $1.5 billion but not exceeding $2 billion; 0.25% to the portion of the daily net assets exceeding $2 billion but not exceeding $2.5 billion; 0.225% to the portion of the daily net assets exceeding $2.5 billion but not exceeding $3 billion; and 0.20% to the portion of the daily net assets exceeding $3 billion.

Pursuant to an Administration Agreement with Morgan Stanley Services Company Inc. (the "Administrator"), an affiliate of the Investment Adviser, the Fund pays an administration fee, accrued daily and payable monthly, by applying the annual rate of 0.05% to the Fund's daily net assets.

Under an 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 Investment Adviser has voluntarily agreed to cap the Fund's operating expenses through June 30, 2009, (excluding fees paid in connection with the U.S. Treasury Temporary Guarantee Program for Money Market Funds) by assuming the Fund's "other expenses" and/or waiving the Fund's advisory fees, and the Administrator has agreed to waive the Fund's administrative fees, to the extent that such operating expenses exceed 0.75% of the average daily net assets of the Fund on an annualized basis.

3. Shareholder Service Plan

Pursuant to a Shareholder Service Plan (the "Plan"), the Fund may pay Morgan Stanley Distributors Inc. (the "Distributor") 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.

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Morgan Stanley U.S. Government Money Market Trust

Notes to Financial Statements  nJanuary 31, 2009 continued

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, 2009, the shareholder servicing fee was accrued at the annual rate of 0.09%.

The Distributor, Investment Adviser and Administrator have voluntarily agreed to waive the Fund's shareholder servicing fee, investment advisory fee and administration fee, respectively, in order to maintain a minimum distribution yield for the Fund. This waiver may be terminated at any time.

4. Security Transactions and Transactions with Affiliates

The cost of purchases and proceeds from sales/maturities of portfolio securities for the year ended January 31, 2009 aggregated $140,728,561,899 and $140,081,452,217, respectively.

Morgan Stanley Trust, an affiliate of the Investment Adviser, Administrator and Distributor, is the Fund's transfer agent.

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, 2009 included in Trustees' fees and expenses in the Statement of Operations amounted to $5,917. At January 31, 2009, the Fund had an accrued pension liability of $59,067 which is included in accrued expenses 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 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 net asset value of the Fund.

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Morgan Stanley U.S. Government Money Market Trust

Notes to Financial Statements  nJanuary 31, 2009 continued

5. Shares of Beneficial Interest

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

	FOR THE YEAR ENDED JANUARY 31, 2009			FOR THE YEAR ENDED JANUARY 31, 2008
Shares sold		4,071,990,363			1,602,357,214
Shares issued in reinvestment of dividends and distributions		19,236,531			33,757,219
		4,091,226,894			1,636,114,433
Shares redeemed		(3,364,275,728	)		(1,495,546,908	)
Net increase in shares outstanding		726,951,166			140,567,525

6. Expense Offset

The expense offset represents a reduction of the fees and expenses for interest earned on cash balances maintained by the Fund with the transfer agent and custodian.

7. Risks Relating to Certain Financial Instruments

The Fund may invest in 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; rather, they are supported by the right of the issuer to borrow from the Treasury.

On September 7, 2008, the Federal Housing Agency ("FHFA") was appointed as conservator of FNMA and FHLMC. In addition, 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.

8. Federal Income Tax Status

The amount of dividends and distributions from net investment income and net realized capital gains are determined in accordance with federal income tax regulations which may differ from generally accepted accounting principles. These "book/tax" differences are either considered temporary or permanent in nature. To the extent these differences are permanent in nature, such amounts are reclassified within the capital accounts based on their federal tax-basis treatment; temporary differences do not require reclassification. Dividends and distributions which exceed net investment income and net realized capital gains for tax purposes are reported as distributions of paid-in-capital.

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Morgan Stanley U.S. Government Money Market Trust

Notes to Financial Statements  nJanuary 31, 2009 continued

The tax character of distributions paid was as follows:

	FOR THE YEAR ENDED JANUARY 31, 2009			FOR THE YEAR ENDED JANUARY 31, 2008
Ordinary income	$	19,376,219		$	33,892,436
Long-term capital gains		450			—
Total distributions	$	19,376,669		$	33,892,436
As of January 31, 2009, the tax-basis components of accumulated earnings were as follows:
Undistributed ordinary income	$	160,439
Undistributed long-term gains		—
Net accumulated earnings		160,439
Post-October losses		(1,474	)
Temporary differences		(61,029	)
Net unrealized appreciation		—
Total accumulated earnings	$	97,936

As of January 31, 2009, the Fund had temporary book/tax differences attributable to post-October losses (capital losses incurred after October 31 within the taxable year which are deemed to arise on the first business day of the Fund's next taxable year) and nondeductible expenses.

Permanent differences, primarily due to nondeductible expenses, resulted in the following reclassifications among the Fund's components of net assets at January 31, 2009:

ACCUMULATED UNDISTRIBUTED NET INVESTMENT INCOME		DISTRIBUTIONS IN EXCESS OF NET REALIZED GAIN			PAID-IN-CAPITAL
$	2,758	$	(2,758	)		—

9. Fair Valuation Measurements

The Fund adopted FASB Statement of Financial Accounting Standards No. 157, Fair ValueMeasurements ("SFAS 157"), effective February 1, 2008. In accordance with SFAS 157, fair value is defined as the price 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. SFAS 157 establishes a three-tier hierarchy to distinguish between (1) inputs that reflect the assumptions market participants would use in pricing 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 pricing an asset or liability developed based on

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Morgan Stanley U.S. Government Money Market Trust

Notes to Financial Statements  nJanuary 31, 2009 continued

the best information available in the circumstances (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 — 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)

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 as of January 31, 2009 in valuing the Fund's investments carried at value:

			FAIR VALUE MEASUREMENTS AT JANUARY 31, 2009 USING
	TOTAL		QUOTED PRICES IN ACTIVE MARKET FOR IDENTICAL ASSETS (LEVEL 1)		SIGNIFICANT OTHER OBSERVABLE INPUTS (LEVEL 2)		SIGNIFICANT UNOBSERVABLE INPUTS (LEVEL 3)
Investments in Securities	$	1,591,320,961		—	$	1,591,320,961		—

10. Accounting Pronouncement

On March 19, 2008, FASB released Statement of Financial Accounting Standards No. 161, Disclosures about Derivative Instruments and Hedging Activities, an amendment of FASB Statement No. 133 ("SFAS 161"). SFAS 161 requires qualitative disclosures about objectives and strategies for using derivatives, quantitative disclosures about fair value amounts of and gains and losses on derivative instruments, and disclosures about credit- risk-related contingent features in derivative agreements. The application of SFAS 161 is required for fiscal years beginning after November 15, 2008 and interim periods within those fiscal years. At this time, management is evaluating the implications of SFAS 161 and its impact on the Fund's financial statements has not yet been determined.

11. Guarantee Program for Money Market Funds

On September 29, 2008, the Trustees approved the participation by the Fund in the U.S. Treasury's Temporary Guarantee Program for Money Market Funds (the "Program"). Under this Program, the U.S.

16

Morgan Stanley U.S. Government Money Market Trust

Notes to Financial Statements  nJanuary 31, 2009 continued

Treasury will guarantee to investors that they will receive $1.00 for each money market fund share held as of close of business on September 19, 2008. Eligible funds must be regulated under Rule 2a-7 of the Act, must maintain a stable share price of $1.00 and must be publicly offered and registered with the Securities and Exchange Commission ("SEC"). To participate in the Program, eligible funds must pay a fee. While the Program protects the accounts of investors, each money market fund makes the decision to sign up for the Program. Investors cannot sign up for the Program individually. The Program was in effect for an initial three month term, expiring December 18, 2008. On November 24, 2008, the U.S. Treasury announced an extension of the Program through April 30, 2009. All money market funds that currently participate in the Program and meet the extension requirements are eligible to continue to participate for an additional fee. The Fund has met the requirements and continues to participate in this Program. The Program will continue to provide coverage to shareholders up to amounts that they held in participating money market funds as of the close of business on September 19, 2008. The Secretary of the Treasury has the option to extend the Program up to the close of business on September 18, 2009.

17

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,
	2009			2008			2007			2006			2005
Selected Per Share Data:
Net asset value, beginning of period	$	1.00		$	1.00		$	1.00		$	1.00		$	1.00
Net investment income from investment operations		0.015			0.044			0.044			0.027			0.008
Less dividends from net investment income		(0.015	)(1)		(0.044	)(1)		(0.044	)(1)		(0.027	)		(0.008	)
Net asset value, end of period	$	1.00		$	1.00		$	1.00		$	1.00		$	1.00
Total Return		1.54	%		4.50	%		4.49	%		2.71	%		0.78	%
Ratios to Average Net Assets:
Total expenses (before expense offset)		0.61	%(2)(3)		0.75	%		0.74	%(3)		0.75	%(3)		0.73	%
Net investment income		1.37	%(2)(3)		4.36	%		4.36	%(3)		2.62	%(3)		0.74	%
Supplemental Data:
Net assets, end of period, in millions	$	1,647		$	920		$	779		$	938		$	1,123

(1)  Includes capital gain distributions of less than $0.001.

(2)  Reflects fees paid in connection with the U.S. Treasury Guarantee Program for Money Market Funds. This fee had an effect of 0.02%. (See Note 11).

(3)  If the Fund had borne all its expenses that were reimbursed or waived by the Investment Adviser and Administrator, the annualized expense and net investment income ratios, before expense offset, would have been as follows:

PERIOD ENDED	EXPENSE RATIO			NET INVESTMENT INCOME RATIO
January 31, 2009		0.62	%		1.36	%
January 31, 2007		0.80			4.30
January 31, 2006		0.76			2.60

See Notes to Financial Statements
18

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:

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, 2009, 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, and the financial highlights for each of the five years in the period then ended. These financial statements and financial highlights are the responsibility of the Fund's management. Our responsibility is to express an opinion on these financial statements and financial highlights based on our audits.

We conducted our audits in accordance with the standards of the Public Company Accounting Oversight Board (United States). Those standards require that we plan and perform the audit to obtain reasonable assurance about whether the financial statements and financial highlights are free of material misstatement. The Fund is not required to have, nor were we engaged to perform, an audit of its internal control over financial reporting. Our audits included consideration of internal control over financial reporting as a basis for designing audit procedures that are appropriate in the circumstances, 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. An audit also includes examining, on a test basis, evidence supporting the amounts and disclosures in the financial statements, assessing the accounting principles used and significant estimates made by management, as well as evaluating the overall financial statement presentation. Our procedures included confirmation of securities owned as of January 31, 2009, by correspondence with the custodian. We believe that our audits provide a reasonable basis for our opinion.

In our opinion, the financial statements and financial highlights referred to above present fairly, in all material respects, the financial position of Morgan Stanley U.S. Government Money Market Trust as of January 31, 2009, 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 the financial highlights for each of the five years in the period then ended, in conformity with accounting principles generally accepted in the United States of America.

Deloitte & Touche LLP
New York, New York
March 25, 2009

19

Morgan Stanley U.S. Government Money Market Trust

An Important Notice Concerning Our U.S. Privacy Policy (unaudited)

We are required by federal law to provide you with a copy of our Privacy Policy annually.

The following Policy applies to current and former individual investors in Morgan Stanley Advisor funds. This Policy is not applicable to partnerships, corporations, trusts or other non-individual clients or account holders. Please note that we may amend this Policy at any time, and will inform you of any changes to this Policy as required by law.

We Respect Your Privacy

We appreciate that you have provided us with your personal financial information. We strive to maintain the privacy of such information while we help you achieve your financial objectives. This Policy describes what non-public personal information we collect about you, why we collect it, and when we may share it with others. We hope this Policy will help you understand how we collect and share non-public personal information that we gather about you. Throughout this Policy, we refer to the non-public information that personally identifies you or your accounts as "personal information."

1. What Personal Information Do We Collect About You?

To serve you better and manage our business, it is important that we collect and maintain accurate information about you. We may obtain this information from applications and other forms you submit to us, from your dealings with us, from consumer reporting agencies, from our Web sites and from third parties and other sources.

For example:

n  We may collect information such as your name, address, e-mail address, telephone/fax numbers, assets, income and investment objectives through applications and other forms you submit to us.

n  We may obtain information about account balances, your use of account(s) and the types of products and services you prefer to receive from us through your dealings and transactions with us and other sources.

n  We may obtain information about your creditworthiness and credit history from consumer reporting agencies.

n  We may collect background information from and through third-party vendors to verify representations you have made and to comply with various regulatory requirements.

n  If you interact with us through our public and private Web sites, we may collect information that you provide directly through online communications (such as an e-mail address). We may also collect information about your Internet service provider, your domain name, your computer's operating system and Web browser, your use of our Web sites and your product and service

20

Morgan Stanley U.S. Government Money Market Trust

An Important Notice Concerning Our U.S. Privacy Policy (unaudited) continued

preferences, through the use of "cookies." "Cookies" recognize your computer each time your return to one of our sites, and help to improve our sites' content and personalize your experience on our sites by, for example, suggesting offerings that may interest you. Please consult the Terms of Use of these sites for more details on our use of cookies.

2. When Do We Disclose Personal Information We Collect About You?

To provide you with the products and services you request, to serve you better and to manage our business, we may disclose personal information we collect about you to our affiliated companies and to non-affiliated third parties as required or permitted by law.

A. Information We Disclose to Our Affiliated Companies. We do not disclose personal information that we collect about you to our affiliated companies except to enable them to provide services on our behalf or as otherwise required or permitted by law.

B. Information We Disclose to Third Parties. We do not disclose personal information that we collect about you to non-affiliated third parties except to enable them to provide services on our behalf, to perform joint marketing agreements with other financial institutions, or as otherwise required or permitted by law. For example, some instances where we may disclose information about you to nonaffiliated third parties include: for servicing and processing transactions, to offer our own products and services, to protect against fraud, for institutional risk control, to respond to judicial process or to perform services on our behalf. When we share personal information with these companies, they are required to limit their use of personal information to the particular purpose for which it was shared and they are not allowed to share personal information with others except to fulfill that limited purpose.

3. How Do We Protect the Security and Confidentiality of Personal Information We Collect About You?

We maintain physical, electronic and procedural security measures to help safeguard the personal information we collect about you. We have internal policies governing the proper handling of client information. Third parties that provide support or marketing services on our behalf may also receive personal information, and we require them to adhere to confidentiality standards with respect to such information.

21

Morgan Stanley U.S. Government Money Market Trust

Trustee and Officer Information (unaudited)

Independent Trustees:

Name, Age and Address of Independent Trustee	Position(s) Held with Registrant	Term of Office and Length of Time Served*	Principal Occupation(s) During Past 5 Years	Number of Portfolios in Fund Complex Overseen by Independent Trustee**		Other Directorships Held by Independent Trustee
Frank L. Bowman (64) c/o Kramer Levin Naftalis & Frankel LLP Counsel to the Independent Trustees 1177 Avenue of the Americas New York, NY 10036	Trustee	Since August 2006	President, Strategic Decisions, LLC (consulting) (since February 2009); Director or Trustee of various Retail Funds and Institutional Funds (since August 2006); Chairperson of the Insurance Sub-Committee of the Compliance and Insurance Committee (since February 2007); served as President and Chief Executive Officer of the Nuclear Energy Institute (policy organization) through November 2008; retired as Admiral, U.S. Navy in January 2005 after serving over 8 years as Director of the Naval Nuclear Propulsion Program and Deputy Administrator — Naval Reactors in the National Nuclear Security Administration at the U.S. Department of Energy (1996-2004). Knighted as Honorary Knight Commander of the Most Excellent Order of the British Empire; Awarded the Officer de l'Orde National du Mérite by the French Government.		168	Director of the Armed Services YMCA of the USA; member, BP America External Advisory Council (energy); member, National Academy of Engineers.
Michael Bozic (68) c/o Kramer Levin Naftalis & Frankel LLP Counsel to the Independent Trustees 1177 Avenue of the Americas New York, NY 10036	Trustee	Since April 1994	Private investor; Chairperson of the Compliance and Insurance Committee (since October 2006); Director or Trustee of the Retail Funds (since April 1994) and Institutional Funds (since July 2003); formerly, Chairperson of the Insurance Committee (July 2006-September 2006); Vice Chairman of Kmart Corporation (December 1998-October 2000), Chairman and Chief Executive Officer of Levitz Furniture Corporation (November 1995-November 1998) and President and Chief Executive Officer of Hills Department Stores (May 1991-July 1995); variously Chairman, Chief Executive Officer, President and Chief Operating Officer (1987-1991) of the Sears Merchandise Group of Sears, Roebuck & Co.		170	Director of various business organizations.

22

Morgan Stanley U.S. Government Money Market Trust

Trustee and Officer Information (unaudited) continued

Name, Age and Address of Independent Trustee	Position(s) Held with Registrant	Term of Office and Length of Time Served*	Principal Occupation(s) During Past 5 Years	Number of Portfolios in Fund Complex Overseen by Independent Trustee**		Other Directorships Held by Independent Trustee
Kathleen A. Dennis (55) c/o Kramer Levin Naftalis & Frankel LLP Counsel to the Independent Trustees 1177 Avenue of the Americas New York, NY 10036	Trustee	Since August 2006	President, Cedarwood Associates (mutual fund and investment management) (since July 2006); Chairperson of the Money Market and Alternatives Sub-Committee of the Investment Committee (since October 2006) and Director or Trustee of various Retail Funds and Institutional Funds (since August 2006); formerly, Senior Managing Director of Victory Capital Management (1993-2006).		168	Director of various non-profit organizations.
Dr. Manuel H. Johnson (60) c/o Johnson Smick Group, Inc. 888 16th Street, N.W. Suite 740 Washington, D.C. 20006	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 the Retail Funds (since July 1991) and Institutional Funds (since July 2003); 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.		170	Director of NVR, Inc. (home construction); Director of Evergreen Energy.
Joseph J. Kearns (66) c/o Kearns & Associates LLC PMB754 23852 Pacific Coast Highway Malibu, CA 90265	Trustee	Since August 1994	President, Kearns & Associates LLC (investment consulting); Chairperson of the Audit Committee (since October 2006) and Director or Trustee of the Retail Funds (since July 2003) and Institutional Funds (since August 1994); formerly, Deputy Chairperson of the Audit Committee (July 2003-September 2006) and Chairperson of the Audit Committee of the Institutional Funds (October 2001-July 2003); CFO of the J. Paul Getty Trust.		171	Director of Electro Rent Corporation (equipment leasing) and The Ford Family Foundation.

23

Morgan Stanley U.S. Government Money Market Trust

Trustee and Officer Information (unaudited) continued

Name, Age and Address of Independent Trustee	Position(s) Held with Registrant	Term of Office and Length of Time Served*	Principal Occupation(s) During Past 5 Years	Number of Portfolios in Fund Complex Overseen by Independent Trustee**		Other Directorships Held by Independent Trustee
Michael F. Klein (50) c/o Kramer Levin Naftalis & Frankel LLP Counsel to the Independent Trustees 1177 Avenue of the Americas New York, NY 10036	Trustee	Since August 2006	Managing Director, Aetos Capital, LLC (since March 2000) and Co-President, Aetos Alternatives Management, LLC (since January 2004); Chairperson of the Fixed Income Sub-Committee of the Investment Committee (since October 2006) and Director or Trustee of various Retail Funds and Institutional Funds (since August 2006); formerly, Managing Director, Morgan Stanley & Co. Inc. and Morgan Stanley Dean Witter Investment Management, President, Morgan Stanley Institutional Funds (June 1998-March 2000) and Principal, Morgan Stanley & Co. Inc. and Morgan Stanley Dean Witter Investment Management (August 1997-December 1999).		168	Director of certain investment funds managed or sponsored by Aetos Capital, LLC. Director of Sanitized AG and Sanitized Marketing AG (specialty chemicals).
Michael E. Nugent (72) c/o Triumph Capital, L.P. 445 Park Avenue New York, NY 10022	Chairperson of the Board and Trustee	Chairperson of the Boards since July 2006 and Trustee since July 1991	General Partner, Triumph Capital, L.P. (private investment partnership); Chairperson of the Boards of the Retail Funds and Institutional Funds (since July 2006); Director or Trustee of the Retail Funds (since July 1991) and Institutional Funds (since July 2001); formerly, Chairperson of the Insurance Committee (until July 2006).		170	None.

24

Morgan Stanley U.S. Government Money Market Trust

Trustee and Officer Information (unaudited) continued

Name, Age and Address of Independent Trustee	Position(s) Held with Registrant	Term of Office and Length of Time Served*	Principal Occupation(s) During Past 5 Years	Number of Portfolios in Fund Complex Overseen by Independent Trustee**		Other Directorships Held by Independent Trustee
W. Allen Reed (61) † c/o Kramer Levin Naftalis & Frankel LLP Counsel to the Independent Trustees 1177 Avenue of the Americas New York, NY 10036	Trustee	Since August 2006	Chairperson of the Equity Sub-Committee of the Investment Committee (since October 2006) and Director or Trustee of various Retail Funds and Institutional 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).		168	Director of Temple-Inland Industries (packaging and forest products); Director of Legg Mason, Inc. and Director of the Auburn University Foundation.
Fergus Reid (76) c/o Lumelite Plastics Corporation 85 Charles Colman Blvd. Pawling, NY 12564	Trustee	Since June 1992	Chairman of Lumelite Plastics Corporation; Chairperson of the Governance Committee and Director or Trustee of the Retail Funds (since July 2003) and Institutional Funds (since June 1992).		171	Trustee and Director of certain investment companies in the JPMorgan Funds complex managed by JP Morgan Investment Management Inc.

Interested Trustee:

Name, Age and Address of Interested Trustee	Position(s) Held with Registrant	Term of Office and Length of Time Served*	Principal Occupation(s) During Past 5 Years	Number of Portfolios in Fund Complex Overseen by Interested Trustee**		Other Directorships Held by Interested Trustee
James F. Higgins (61) c/o Morgan Stanley Trust Harborside Financial Center Plaza Two Jersey City, NJ 07311	Trustee	Since June 2000	Director or Trustee of the Retail Funds (since June 2000) and Institutional Funds (since July 2003); Senior Advisor of Morgan Stanley (since August 2000).		169	Director of AXA Financial, Inc. and TheEquitable Life Assurance Society of the United States (financial services).

*  This is the earliest date the Trustee began serving the funds advised by Morgan Stanley Investment Advisors Inc. (the "Investment Adviser") (the "Retail Funds") or the funds advised by Morgan Stanley Investment Management Inc. and Morgan Stanley AIP GP LP (the "Institutional Funds").

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

  †  For the period September 26, 2008 through February 5, 2008 W. Allen Reed was an Interested Trustee. At all other times covered by this report, Mr. Reed was an Independent Trustee.

25

Morgan Stanley U.S. Government Money Market Trust

Trustee and Officer Information (unaudited) continued

Executive Officers:

Name, Age and Address of Executive Officer	Position(s) Held with Registrant	Term of Office and Length of Time Served*	Principal Occupation(s) During Past 5 Years
Randy Takian (34) 522 Fifth Avenue New York, NY 10036	President and Principal Executive Officer	President and Principal Executive Officer (since September 2008)	President and Principal Executive Officer (since September 2008) of funds in the Fund Complex; President and Chief Executive Officer of Morgan Stanley Services Company Inc. (since September 2008). President of the Investment Adviser (since July 2008). Head of the Retail and Intermediary business within Morgan Stanley Investment Management (since July 2008). Head of Liquidity and Bank Trust business (since July 2008) and the Latin American franchise (since July 2008) at Morgan Stanley Investment Management. Managing Director, Director and/or Officer of the Investment Adviser and various entities affiliated with the Investment Adviser. Formerly Head of Strategy and Product Development for the Alternatives Group and Senior Loan Investment Management. Formerly with Bank of America (July 1996-March 2006), most recently as Head of the Strategy, Mergers and Acquisitions team for Global Wealth and Investment Management.
Kevin Klingert (46) 522 Fifth Avenue New York, NY 10036	Vice President	Since June 2008	Global Head, Chief Operating Officer and acting Chief Investment Officer of the Global Fixed Income Group of Morgan Stanley Investment Management Inc. and the Investment Adviser (since April 2008). Head of Global Liquidity Portfolio Management and co-Head of Liquidity Credit Research of Morgan Stanley Investment Management (since December 2007). Managing Director of Morgan Stanley Investment Management Inc. and the Investment Adviser (since December 2007). Previously, Managing Director on the Management Committee and head of Municipal Portfolio Management and Liquidity at BlackRock (October 1991 to January 2007).
Amy R. Doberman (47) 522 Fifth Avenue New York, NY 10036	Vice President	Since July 2004	Managing Director of Morgan Stanley Investment Management (since July 2004); Vice President of the Retail Funds and Institutional Funds (since July 2004); Vice President of the Van Kampen Funds (since August 2004); Secretary (since February 2006) and Managing Director (since July 2004) of the Investment Adviser and various entities affiliated with the Investment Adviser. Formerly, Managing Director and General Counsel — Americas, UBS Global Asset Management (July 2000 to July 2004).
Carsten Otto (45) 522 Fifth Avenue New York, NY 10036	Chief Compliance Officer	Since October 2004	Managing Director and Global Head of Compliance for Morgan Stanley Investment Management (since April 2007) and Chief Compliance Officer of the Retail Funds and Institutional Funds (since October 2004). Formerly, U.S. Director of Compliance (October 2004-April 2007) and Assistant Secretary and Assistant General Counsel of the Retail Funds.
Stefanie V. Chang Yu (42) 522 Fifth Avenue New York, NY 10036	Vice President	Since December 1997	Managing Director of the Investment Adviser and various entities affiliated with the Investment Adviser; Vice President of the Retail Funds (since July 2002) and Institutional Funds (since December 1997). Formerly, Secretary of various entities affiliated with the Investment Adviser.

26

Morgan Stanley U.S. Government Money Market Trust

Trustee and Officer Information (unaudited) continued

Name, Age and Address of Executive Officer	Position(s) Held with Registrant	Term of Office and Length of Time Served*	Principal Occupation(s) During Past 5 Years
Francis J. Smith (43) c/o Morgan Stanley Trust Harborside Financial Center, Plaza Two, Jersey City, NJ 07311	Treasurer and Chief Financial Officer	Treasurer since July 2003 and Chief Financial Officer since September 2002	Executive Director of the Investment Adviser and various entities affiliated with the Investment Adviser; Treasurer and Chief Financial Officer of the Retail Funds (since July 2003). Formerly, Vice President of the Retail Funds (September 2002-July 2003).
Mary E. Mullin (42) 522 Fifth Avenue New York, NY 10036	Secretary	Since June 1999	Executive Director of the Investment Adviser and various entities affiliated with the Investment Adviser; Secretary of the Retail Funds (since July 2003) and Institutional Funds (since June 1999).

* This is the earliest date the Officer began serving the Retail Funds or Institutional Funds.

2009 Federal Tax Notice (Unaudited)

For Federal income tax purposes, the following information is furnished with respect to the distributions paid by the Fund during its taxable year ended January 31, 2009. The Fund designated and paid $450 as a long-term capital gain distribution. 55.67% of the Fund's dividends was attributable to qualifying U.S. Government obligations. (Please consult your tax advisor to determine if any portion of the dividends you received is exempt from state income tax.)

For Federal income tax purposes, the following information is furnished with respect to the Fund's earnings for its taxable year ended January 31, 2009. For non-U.S. residents, the Fund may designate up to a maximum of $31,238 as qualifying as short-term capital gain dividends.

In January, the Fund provides tax information to shareholders for the preceding calendar year.

27

Trustees

Frank L. Bowman
Michael Bozic
Kathleen A. Dennis
James F. Higgins
Dr. Manuel H. Johnson
Joseph J. Kearns
Michael F. Klein
Michael E. Nugent
W. Allen Reed
Fergus Reid

Officers

Michael E. Nugent
Chairperson of the Board

Randy Takian
President and Principal Executive Officer

Kevin Klingert
Vice President

Amy R. Doberman
Vice President

Carsten Otto
Chief Compliance Officer

Stefanie V. Chang Yu
Vice President

Francis J. Smith
Treasurer and Chief Financial Officer

Mary E. Mullin
Secretary

Transfer Agent

Morgan Stanley Trust
Harborside Financial Center, Plaza Two
Jersey City, New Jersey 07311

Independent Registered Public Accounting Firm

Deloitte & Touche LLP
Two World Financial Center
New York, New York 10281

Legal Counsel

Clifford Chance US LLP
31 West 52nd Street
New York, New York 10019

Counsel to the Independent Trustees

Kramer Levin Naftalis & Frankel LLP
1177 Avenue of the Americas
New York, New York 10036

Investment Adviser

Morgan Stanley Investment Advisors Inc.
522 Fifth Avenue
New York, New York 10036

INVESTMENT MANAGEMENT

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) 869-NEWS.

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

Morgan Stanley Distributors Inc., member FINRA.

© 2009 Morgan Stanley

DWGANN
IU09-01170P-Y01/09

Morgan Stanley
U.S. Government
Money Market Trust

Annual Report

January 31, 2009

Item 2.  Code of Ethics.

(a)           The Fund 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 Fund 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 Fund’s Code of Ethics is attached hereto as Exhibit 12 A.

(2)           Not applicable.

(3)           Not applicable.

Item 3.  Audit Committee Financial Expert.

The Fund’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:

2009

	Registrant			Covered Entities(1)
Audit Fees	$	27,650		N/A
Non-Audit Fees
Audit-Related Fees	$	4,940	(2)	$	6,418,000	(2)
Tax Fees	$	—	(3)	$	881,000	(4)
All Other Fees	$			$
Total Non-Audit Fees	$	4,940		$	7,299,000
Total	$	32,590		$	7,299,000

2008

	Registrant			Covered Entities(1)
Audit Fees	$	26,950		N/A
Non-Audit Fees
Audit-Related Fees	$	4,532	(2)	$	6,164,000	(2)
Tax Fees	$	—	(3)	$	1,002,000	(4)
All Other Fees	$			$		(5)
Total Non-Audit Fees	$	4,532		$	7,166,000
Total	$	31,482		$	7,166,000

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 RETAIL AND INSTITUTIONAL FUNDS

AS ADOPTED AND AMENDED JULY 23, 2004,(1)

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.

(1)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.

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.

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-SAR 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 Chief Financial Officer and must include a detailed description of the services to be

rendered.  The Fund’s Chief Financial 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 will be submitted to the Audit Committee by both the Independent Auditors and the Fund’s Chief Financial Officer, and must include a joint statement as to whether, in their view, the request or application is consistent with the SEC’s rules on auditor independence.

The Audit Committee has designated the Fund’s Chief Financial 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 Chief Financial Officer will report to the Audit Committee on a periodic basis on the results of its monitoring.  Both the Fund’s Chief Financial 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 Chief Financial 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 Independence Standards Board No. 1, 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 Retail Funds

Morgan Stanley Investment Advisors Inc.

Morgan Stanley & Co. Incorporated

Morgan Stanley DW Inc.

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

Van Kampen Asset Management

Morgan Stanley Services Company, Inc.

Morgan Stanley Distributors Inc.

Morgan Stanley Trust FSB

Morgan Stanley Institutional Funds

Morgan Stanley Investment Management Inc.

Morgan Stanley Investment Advisors 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 & Co. Incorporated

Morgan Stanley Distribution, Inc.

Morgan Stanley AIP GP LP

Morgan Stanley Alternative Investment Partners LP

(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 Fund has a separately-designated standing audit committee established in accordance with Section 3(a)(58)(A) of the Exchange Act whose members are: Joseph Kearns, Michael Nugent and 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

Not applicable.

Item 11. Controls and Procedures

(a)  The Fund’s principal executive officer and principal financial officer have concluded that the Fund’s disclosure controls and procedures are sufficient to ensure that information required to be disclosed by the Fund 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. Exhibits

(a) The Code of Ethics for Principal Executive and Senior Financial Officers is attached hereto.

(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/ Randy Takian

Randy Takian

Principal Executive Officer

March 19, 2009

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/ Randy Takian

Randy Takian

Principal Executive Officer

March 19, 2009

/s/ Francis Smith

Francis Smith

Principal Financial Officer

March 19, 2009