Filed Pursuant to Rule 424(b)(3)
Registration No. 333-239499

PROSPECTUS

Up to $12,000,000

Common Stock

We have entered into a sales agreement, or the Sales Agreement, with SVB Leerink LLC, or SVB Leerink, dated June 26, 2020, relating to shares of our common stock, par value $0.001 per share, offered by this prospectus. In accordance with the terms of the Sales Agreement, we may offer and sell shares of our common stock having an aggregate offering price of up to $12,000,000 from time to time through SVB Leerink, acting as our agent.

Our common stock is listed on the Nasdaq Global Market under the symbol “TRVI”. On July 1, 2020, the last reported sale price of our common stock on the Nasdaq Global Market was $6.98 per share.

As of June 25, 2020, the aggregate market value of our outstanding common stock held by non-affiliates was approximately $36,516,841, which we calculated based on 17,843,639 shares of outstanding common stock as of June 25, 2020, of which 6,296,007 shares were held by non-affiliates, and a price per share of $5.80 as of June 25, 2020, which is a date within 60 days prior to the date of this prospectus. Pursuant to General Instruction I.B.6 of Form S-3, in no event will we sell, pursuant to the registration statement of which this prospectus forms a part, securities in a public primary offering with a value exceeding one-third of the aggregate market value of our outstanding common stock held by non-affiliates in any 12-month period, so long as the aggregate market value of our outstanding common stock held by non-affiliates remains below $75 million. During the 12 calendar months prior to and including the date of this prospectus, we have not offered or sold any securities pursuant to General Instruction I.B.6 of Form S-3.

Sales of our common stock, if any, under this prospectus may be made in sales deemed to be an “at the market offering” as defined in Rule 415(a)(4) promulgated under the Securities Act of 1933, as amended, or the Securities Act. SVB Leerink is not required to sell any specific number or dollar amount of shares of our common stock but will act as our sales agent and use its commercially reasonable efforts consistent with its normal trading and sales practices and applicable state and federal laws, rules and regulations and the rules of the Nasdaq Global Market to sell on our behalf the shares of common stock requested to be sold by us, on mutually agreed terms between SVB Leerink and us. There is no arrangement for funds to be received in any escrow, trust or similar arrangement.

The compensation payable to SVB Leerink for sales of common stock sold pursuant to the Sales Agreement will be an amount equal to 3.0% of the gross proceeds from the sale of any shares of common stock under the Sales Agreement. See “Plan of Distribution” beginning on page 15 for additional information regarding the compensation to be paid to SVB Leerink. In connection with the sale of the common stock on our behalf, SVB Leerink will be deemed to be an “underwriter” within the meaning of the Securities Act, and the compensation paid to SVB Leerink will be deemed to be underwriting commissions or discounts. We have also agreed in the Sales Agreement to provide indemnification and contribution to SVB Leerink with respect to certain liabilities, including liabilities under the Securities Act or the Securities Exchange Act of 1934, as amended, or the Exchange Act.

Investing in our common stock involves a high degree of risk. See “Risk Factors” beginning on page 5 of this prospectus and the risk factors in the documents incorporated by reference in this prospectus for a discussion of the factors you should carefully consider before deciding to purchase our common stock.

Neither the Securities and Exchange Commission nor any state securities commission has approved or disapproved of these securities or determined if this prospectus is truthful or complete. Any representation to the contrary is a criminal offense.

SVB Leerink

The date of this prospectus is July 2, 2020

TABLE OF CONTENTS

ABOUT THIS PROSPECTUS	1
PROSPECTUS SUMMARY	3
RISK FACTORS	5
CAUTIONARY NOTE REGARDING FORWARD-LOOKING STATEMENTS	7
USE OF PROCEEDS	8
DILUTION	9
DESCRIPTION OF CAPITAL STOCK	11
PLAN OF DISTRIBUTION	15
LEGAL MATTERS	17
EXPERTS	17
WHERE YOU CAN FIND MORE INFORMATION	18
INFORMATION INCORPORATED BY REFERENCE	19

ABOUT THIS PROSPECTUS

This prospectus is part of a registration statement that we filed with the Securities and Exchange Commission, which we refer to as the SEC or the Commission, utilizing a “shelf” registration process. Under this shelf registration process, we may from time to time offer shares of our common stock having an aggregate offering price of up to $12,000,000 under this prospectus at prices and on terms to be determined by market conditions at the time of offering.

Before buying any of the common stock that we are offering, we urge you to carefully read this prospectus, all of the information contained in the documents incorporated by reference in this prospectus, as well as the additional information described under the headings “Where You Can Find More Information” and “Information Incorporated by Reference.” These documents contain important information that you should consider when making your investment decision.

This prospectus contains or incorporates by reference summaries of certain provisions contained in some of the documents described herein, but all such summaries are qualified in their entirety by the actual documents. Copies of some of the documents referred to herein have been or will be filed or have been or will be incorporated by reference as exhibits to the registration statement of which this prospectus forms a part, and you may obtain copies of those documents as described in this prospectus under the heading “Where You Can Find More Information.”

This prospectus describes the specific terms of the common stock we are offering and also adds to, and updates information contained in the documents incorporated by reference into this prospectus. To the extent there is a conflict between the information contained in this prospectus, on the one hand, and the information contained in any document incorporated by reference in this prospectus that was filed with the SEC before the date of this prospectus, on the other hand, you should rely on the information in this prospectus. If any statement in one of these documents is inconsistent with a statement in another document having a later date—for example, a document incorporated by reference in this prospectus—the statement in the document having the later date modifies or supersedes the earlier statement.

We further note that the representations, warranties and covenants made by us in any agreement that is filed as an exhibit to any document that is incorporated by reference herein were made solely for the benefit of the parties to such agreement, including, in some cases, for the purpose of allocating risk among the parties to such agreement, and should not be deemed to be a representation, warranty or covenant to you. Moreover, such representations, warranties or covenants were accurate only as of the date when made. Accordingly, such representations, warranties and covenants should not be relied on as accurately representing the current state of our affairs.

You should rely only on the information contained in or incorporated by reference in this prospectus and in any free writing prospectus we have authorized for use in connection with this offering. Neither we nor SVB Leerink LLC, or SVB Leerink, have authorized anyone to provide you with any information other than that contained or incorporated by reference in this prospectus or in any free writing prospectus that we authorize for use in connection with this offering and to which we have referred you. We and SVB Leerink take no responsibility for, and can provide no assurance as to the reliability of, any other information that others may give you. If anyone provides you with different or inconsistent information, you should not rely on it. This prospectus does not constitute an offer to sell or the solicitation of an offer to buy any securities other than the securities described in this prospectus or an offer to sell or the solicitation of an offer to buy such securities in any circumstances in which such offer or solicitation is unlawful. You should assume that the information appearing in this prospectus, the documents incorporated by reference herein and any free writing prospectus that we have authorized for use in connection with this offering is accurate only as of their respective dates. Our business, financial condition, results of operations and prospects may have changed materially since those dates.

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Other than in the United States, no action has been taken by us or SVB Leerink that would permit a public offering of the securities offered by this prospectus in any jurisdiction where action for that purpose is required. The securities offered by this prospectus may not be offered or sold, directly or indirectly, nor may this prospectus or any other offering material or advertisements in connection with the offer and sale of any such securities be distributed or published in any jurisdiction, except under circumstances that will result in compliance with the applicable rules and regulations of that jurisdiction. Persons into whose possession this prospectus comes are advised to inform themselves about and to observe any restrictions relating to the offering and the distribution of this prospectus.

Unless the context otherwise indicates, references in this prospectus to “we,” “our” and “us” refer, collectively, to Trevi Therapeutics, Inc., a Delaware corporation, and its subsidiary.

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PROSPECTUS SUMMARY

This summary highlights selected information contained elsewhere in, or incorporated by reference into, this prospectus. Because it is only a summary, it does not contain all of the information that you should consider before investing in our common stock, and it is qualified in its entirety by, and should be read in conjunction with, the more detailed information appearing elsewhere in this prospectus, any free writing prospectus that we have authorized for use in connection with this offering and the documents incorporated by reference in this prospectus. You should read all such documents carefully, and you should pay special attention to the information contained under the caption entitled “Risk Factors” in this prospectus, in our Annual Report on Form 10-K for the year ended December 31, 2019, in our Quarterly Report on Form 10-Q for the quarter ended March 31, 2020, in any subsequent Annual Reports on Form 10-K and Quarterly Reports on Form 10-Q and in our other reports filed from time to time with the SEC, which are incorporated by reference into this prospectus, before deciding to buy shares of our common stock.

Overview

We are a clinical-stage biopharmaceutical company focused on the development and commercialization of nalbuphine ER to treat serious neurologically mediated conditions. We are developing nalbuphine ER for the treatment of chronic pruritus, chronic cough in patients with idiopathic pulmonary fibrosis, and levodopa-induced dyskinesia in patients with Parkinson’s disease. These conditions share a common pathophysiology that is mediated through opioid receptors in the central and peripheral nervous systems. Due to nalbuphine’s mechanism of action as a modulator of opioid receptors, we believe nalbuphine ER has the potential to be effective in treating each of these conditions. Our ongoing clinical trials of nalbuphine ER include a Phase 2b/3 clinical trial, which we refer to as the PRISM trial, in patients with severe pruritus associated with prurigo nodularis. If successful, we expect that we will use the PRISM trial and an additional Phase 3 clinical trial that we plan to conduct to support the submission of a new drug application to the United States Food and Drug Administration and a marketing authorization application to the European Medicines Agency for nalbuphine ER for the treatment of pruritus associated with prurigo nodularis.

Corporate Information

We were incorporated in Delaware on March 17, 2011 under the name Trevi Therapeutics, Inc. Our principal executive offices are located at 195 Church Street, 14^th Floor, New Haven, Connecticut, 06510, and our telephone number is (203) 304-2499. Our website is located at www.trevitherapeutics.com. Information found on, or accessible through, our website is not a part of, and is not incorporated into, this prospectus, and you should not consider it part of this prospectus. Our website address is included in this document as an inactive textual reference only.

Information concerning our business and our prospects is included in the documents that we file with the SEC as a reporting company under the Exchange Act, which are accessible at www.sec.gov, and on our website.

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THE OFFERING

Common Stock Offered by Us Shares of our common stock having an aggregate offering price of up to $12,000,000.

Common Stock to Be Outstanding After This Offering Up to 19,553,767 shares, assuming sales of 1,719,197 shares of our common stock in this offering at a price of $6.98 per share, which was the last reported sale price of our common stock on the Nasdaq Global Market on July 1, 2020. The actual number of shares issued will vary depending on the sales price under this offering.

Manner of Offering “At the market offering” that may be made from time to time through our sales agent, SVB Leerink. See “Plan of Distribution” on page 15.

Use of Proceeds We intend to use the net proceeds from this offering, if any, to fund the clinical development of nalbuphine ER and for working capital and other general corporate purposes. See “Use of Proceeds.”

Risk Factors Investing in our common stock involves a high degree of risk. You should read the “Risk Factors” section of this prospectus beginning on page 5 as well as those risk factors that are incorporated by reference in this prospectus for a discussion of factors to consider carefully before deciding to invest in our common stock.

Nasdaq Global Market Symbol “TRVI.”

The number of shares of our common stock to be outstanding after this offering is based on 17,834,570 shares of our common stock outstanding as of March 31, 2020. The number of shares of our common stock to be outstanding as used throughout this prospectus, unless otherwise indicated, excludes:

• 2,205,535 shares of common stock issuable upon exercise of stock options outstanding as of March 31, 2020 at a weighted-average exercise price of $6.03 per share;

• 1,131,554 shares of common stock reserved as of March 31, 2020 for future issuance under our 2019 Stock Incentive Plan; and

• 333,451 shares of common stock reserved as of March 31, 2020 for future issuance under our 2019 Employee Stock Purchase Plan.

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RISK FACTORS

An investment in our common stock involves a high degree of risk. Before deciding whether to invest in our common stock, you should carefully consider the risks described below and those discussed under the caption entitled “Risk Factors” in our Annual Report on Form 10-K for the year ended December 31, 2019, our Quarterly Report on Form 10-Q for the quarter ended March 31, 2020, and any subsequent Annual Reports on Form 10-K and Quarterly Reports on Form 10-Q, which are incorporated by reference in this prospectus, together with other information in this prospectus, the information and documents incorporated by reference herein, and in any free writing prospectus that we have authorized for use in connection with this offering. If any of these risks actually occurs, our business, financial condition, results of operations or cash flow could be seriously harmed. This could cause the trading price of our common stock to decline, resulting in a loss of all or part of your investment.

Risks Related to this Offering

We have broad discretion in the use of the net proceeds from this offering and may not use them effectively.

Our management will have broad discretion in the application of the net proceeds from this offering and could spend the proceeds in ways that do not improve our results of operations or enhance the value of our common stock. The failure by our management to apply these funds effectively could result in financial losses, and these financial losses could have a material adverse effect on our business, cause the price of our common stock to decline and delay the development of our product candidates. Pending their use, we may invest the net proceeds from this offering in a manner that does not produce income or that loses value.

It is not possible to predict the aggregate proceeds resulting from sales made under the Sales Agreement.

Subject to certain limitations in the Sales Agreement, and compliance with applicable law, we have the discretion to deliver a placement notice to SVB Leerink at any time throughout the term of the Sales Agreement. The number of shares that are sold through SVB Leerink after delivering a placement notice will fluctuate based on a number of factors, including the market price of our common stock during the sales period, any limits we may set with SVB Leerink in any applicable placement notice and the demand for our common stock. Because the price per share of each share sold pursuant to the Sales Agreement will fluctuate over time, it is not currently possible to predict the aggregate proceeds to be raised in connection with sales under the sales agreement.

The common stock offered hereby will be sold in “at the market offerings,” and investors who buy shares at different times will likely pay different prices.

Investors who purchase shares in this offering at different times will likely pay different prices, and accordingly may experience different levels of dilution and different outcomes in their investment results. We will have discretion, subject to market demand and the terms of the Sales Agreement, to vary the timing, prices and number of shares sold in this offering. In addition, subject to the final determination by our board of directors or any restrictions we may place in any applicable placement notice, there is no minimum or maximum sales price for shares to be sold in this offering. Investors may experience a decline in the value of the shares they purchase in this offering as a result of sales made at prices lower than the prices they paid.

If you purchase our common stock in this offering, you may incur immediate and substantial dilution in the book value of your shares.

The shares sold in this offering, if any, will be sold from time to time at various prices. However, the expected offering price of our common stock may be substantially higher than the net tangible book value per share of our common stock. Therefore, if you purchase shares of our common stock in this offering, you may pay a price per share that exceeds our as adjusted net tangible book value per share of common stock. Assuming that

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an aggregate of 1,719,197 shares of our common stock are sold at a price of $6.98 per share, which was the last reported sale price of our common stock on the Nasdaq Global Market on July 1, 2020, for aggregate gross proceeds of $12,000,000, and after deducting commissions and estimated offering expenses payable by us, you would experience immediate dilution of $4.00 per share, representing the difference between our as adjusted net tangible book value per share as of March 31, 2020 after giving effect to this offering and the assumed offering price. To the extent outstanding options are exercised, you will experience further dilution. See the section titled “Dilution” below for a more detailed illustration of the dilution you would incur if you participate in this offering.

If you purchase shares of common stock in this offering, you may also experience future dilution as a result of future equity offerings.

To raise additional capital, we may in the future offer additional shares of our common stock or other securities convertible into or exchangeable for our common stock at prices that may not be the same as the price per share in this offering. We may sell shares or other securities in any other offering at a price per share that is less than the price per share paid by any investors in this offering, and investors purchasing shares or other securities in the future could have rights superior to existing stockholders. The price per share at which we sell additional shares of our common stock, or securities convertible or exchangeable into common stock, in future transactions may be higher or lower than the price per share paid by any investors in this offering.

Because we do not anticipate paying any cash dividends on our capital stock in the foreseeable future, capital appreciation, if any, will be your sole source of gain.

We have never declared or paid cash dividends on our capital stock. We currently intend to retain all of our future earnings, if any, to finance the growth and development of our business. In addition, the terms of any future debt agreements that we may enter into may preclude us from paying dividends without the lenders’ consent or at all. As a result, capital appreciation, if any, of our common stock will be your sole source of gain for the foreseeable future.

Sales of a significant number of shares of our common stock in the public markets, or the perception that such sales could occur, could depress the market price of our common stock.

Sales of a substantial number of shares of our common stock in the public market, or the perception in the market that the holders of a large number of shares of our common stock intend to sell shares of our common stock, could reduce the market price of our common stock. Our executive officers and directors and their affiliates and our significant stockholders hold a significant number of shares of our common stock. If such persons sell, or indicate an intention to sell, substantial amounts of our common stock in the public market, the trading price of our common stock could decline. Moreover, holders of a substantial number of shares of our common stock have rights, subject to specified conditions, to require us to file registration statements covering their shares or to include their shares in registration statements that we may file for ourselves or other stockholders.

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CAUTIONARY NOTE REGARDING FORWARD-LOOKING STATEMENTS

This prospectus and the information incorporated by reference in this prospectus include “forward-looking statements” within the meaning of Section 27A of the Securities Act of 1933, as amended, or the Securities Act, and Section 21E of the Exchange Act, which involve substantial risks and uncertainties. All statements, other than statements of historical fact, in this prospectus or the information incorporated by reference in this prospectus, including statements regarding our strategy, future operations, future financial position, future revenues and profitability, projected costs, prospects, plans and objectives of management, are forward-looking statements. The words “anticipate,” “believe,” “estimate,” “expect,” “intend,” “may,” “might,” “plan,” “potential,” “predict,” “project,” “should,” “target,” “would,” “could,” “continue” and similar expressions are intended to identify forward-looking statements, although not all forward-looking statements contain these identifying words.

These forward-looking statements may include, among other things, statements about:

• the impact of the COVID-19 pandemic on our clinical trials, business and operations;

• our ongoing clinical trials, including our Phase 2b/3 PRISM trial of nalbuphine ER for the treatment of pruritus associated with prurigo nodularis;

• our plans to develop and, if approved, subsequently commercialize nalbuphine ER for the treatment of pruritus associated with prurigo nodularis or for other serious neurologically mediated conditions;

• our expectations regarding the timing for the initiation of clinical trials, completion of enrollment of such trials and the reporting of data from such trials;

• the timing of and our ability to submit applications for, and to obtain and maintain regulatory approvals for, nalbuphine ER;

• our expectations regarding our ability to fund our operating expenses and capital expenditure requirements with our cash and cash equivalents;

• our estimates regarding expenses, future revenue, timing of any future revenue, capital requirements and needs for additional financing;

• the impact of government laws and regulations;

• our competitive position;

• our ability to establish and maintain collaborations or obtain additional funding; and

• our intended use of proceeds from this offering.

We may not actually achieve the plans, intentions or expectations disclosed in our forward-looking statements, and you should not place undue reliance on our forward-looking statements. Actual results or events could differ materially from the plans, intentions and expectations disclosed in the forward-looking statements we make. We have included important factors in the cautionary statements included in this prospectus and the documents we incorporate by reference herein, particularly in the section titled “Risk Factors” in this prospectus and in our Annual Report on Form 10-K for the year ended December 31, 2019 and our Quarterly Report on Form 10-Q for the quarterly period ended March 31, 2020, that we believe could cause actual results or events to differ materially from the forward-looking statements that we make. Our forward-looking statements do not reflect the potential impact of any future acquisitions, mergers, dispositions, joint ventures or investments we may make.

You should read this prospectus and the documents we incorporate by reference herein and have filed or incorporated by reference herein completely and with the understanding that our actual future results may differ materially from what we expect. We do not assume any obligation to update any forward-looking statements except as required by applicable law.

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USE OF PROCEEDS

We may issue and sell shares of our common stock having an aggregate offering price of up to $12,000,000 from time to time. Because there is no minimum offering amount required as a condition to close this offering, the actual public offering amount, commissions to SVB Leerink and proceeds to us, if any, are not determinable at this time. There can be no assurance that we will sell any shares under the Sales Agreement.

We currently intend to use the net proceeds from this offering, if any, to fund the clinical development of nalbuphine ER and for working capital and other general corporate purposes.

The amounts and timing of our use of the net proceeds from the sale of securities in this offering, if any, will depend on a number of factors, including the progress of our clinical development of nalbuphine ER, the status of and results from our clinical trials, including our ongoing PRISM trial as well as the additional Phase 3 clinical trial we will need to conduct for nalbuphine ER for pruritus associated with prurigo nodularis, the timing of regulatory submissions and the outcome of regulatory review, as well as any collaborations that we may enter into with third parties and any unforeseen cash needs. As of the date of this prospectus, we cannot specify with certainty all of the particular uses for the net proceeds to us, if any, from this offering. Accordingly, our management will have broad discretion in the timing and application of these proceeds. Pending application of the net proceeds as described above, we intend to temporarily invest the proceeds in short-term, interest-bearing instruments.

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DILUTION

If you invest in our common stock in this offering, your ownership interest will be diluted immediately to the extent of the difference between the price per share of our common stock you pay in this offering and the as adjusted net tangible book value per share of our common stock immediately after giving effect to this offering.

We calculate net tangible book value per share of our common stock by dividing net tangible book value, which we calculate as our total assets less our total liabilities, by the number of outstanding shares of our common stock. Dilution as presented below represents the difference between the assumed price per share paid by purchasers of shares of our common stock in this offering and the as adjusted net tangible book value per share of our common stock after giving effect to this offering. Our historical net tangible book value as of March 31, 2020 was approximately $46.8 million, or $2.62 per share of our common stock.

After giving effect to the assumed sale by us of shares of our common stock pursuant to this prospectus in the aggregate amount of $12,000,000 at an assumed offering price of $6.98 per share, which was the last reported sale price of our common stock on the Nasdaq Global Market on July 1, 2020, and after deducting commissions and estimated offering expenses payable by us, our as adjusted net tangible book value as of March 31, 2020 would have been $58.2 million, or $2.98 per share of our common stock. This represents an immediate increase in the as adjusted net tangible book value of $0.36 per share to our existing stockholders and an immediate dilution in as adjusted net tangible book value of $4.00 per share to new investors participating in this offering. Dilution per share to new investors is determined by subtracting as adjusted net tangible book value per share after this offering from the assumed offering price per share paid by new investors. The following table illustrates this dilution on a per share basis:

Assumed offering price per share			$	6.98
Net tangible book value per share as of March 31, 2020	$	2.62
Increase in net tangible book value per share attributable to new investors purchasing shares in this offering	$	0.36
As adjusted net tangible book value per share after giving effect to this offering			$	2.98
Dilution per share to new investors purchasing shares in this offering			$	4.00

The table above assumes for illustrative purposes that an aggregate of 1,719,197 shares of our common stock are sold pursuant to this prospectus at an offering price of $6.98 per share, which was the last reported sale price of our common stock on the Nasdaq Global Market on July 1, 2020, for aggregate gross proceeds of $12,000,000. The shares of our common stock sold in this offering, if any, will be sold from time to time at various prices. The as adjusted information is illustrative only and will adjust based on the actual price to the public, the actual number of shares sold and other terms of the offering determined at the time shares of our common stock are sold pursuant to this prospectus.

An increase of $1.00 per share in the price at which the shares are sold from the assumed offering price of $6.98 per share shown in the table above, assuming all of our common stock in the aggregate amount of $12,000,000 is sold at that price, would result in an as adjusted net tangible book value per share after the offering of $3.01 per share and would increase the dilution in net tangible book value per share to new investors in this offering to $4.97 per share, after deducting commissions and estimated offering expenses payable by us. A decrease of $1.00 per share in the price at which the shares are sold from the assumed offering price of $6.98 per share shown in the table above, assuming all of our common stock in the aggregate amount of $12,000,000 is sold at that price, would result in an as adjusted net tangible book value per share after the offering of $2.93 per share and would decrease the dilution in net tangible book value per share to new investors in this offering to $3.05 per share, after deducting commissions and estimated offering expenses payable by us.

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The above discussion and table are based on 17,834,570 shares of our common stock issued and outstanding as of March 31, 2020 and excludes the following:

• 2,205,535 shares of common stock issuable upon exercise of stock options outstanding as of March 31, 2020 at a weighted-average exercise price of $6.03 per share;

• 1,131,554 shares of common stock reserved as of March 31, 2020 for future issuance under our 2019 Stock Incentive Plan; and

• 333,451 shares of common stock reserved as of March 31, 2020 for future issuance under our 2019 Employee Stock Purchase Plan.

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DESCRIPTION OF CAPITAL STOCK

The following description of our capital stock is intended as a summary only and therefore is not a complete description of our capital stock. This description is based upon, and is qualified by reference to, our certificate of incorporation, our by-laws and applicable provisions of Delaware corporate law. You should read our certificate of incorporation and by-laws, which are filed as exhibits to the registration statement of which this prospectus forms a part, for the provisions that are important to you.

Our authorized capital stock consists of 200,000,000 shares of common stock and 5,000,000 shares of preferred stock. As of May 31, 2020, 17,834,570 shares of common stock were outstanding and no shares of preferred stock were outstanding.

Common Stock

Annual Meeting. Annual meetings of our stockholders are held on the date designated in accordance with our by-laws. Written notice must be mailed to each stockholder entitled to vote not less than ten nor more than 60 days before the date of the meeting. The presence in person or by proxy of the holders of record of a majority in voting power of our issued and outstanding shares entitled to vote at such meeting constitutes a quorum for the transaction of business at meetings of the stockholders. Special meetings of the stockholders may be called for any purpose by the board of directors and shall be called by the chairman of the board or the secretary upon the written request, stating the purpose of such meeting, of the holders of a majority of the outstanding shares of all classes of capital stock entitled to vote at the meeting. Except as may be otherwise provided by applicable law, our certificate of incorporation or our by-laws, all elections shall be decided by a plurality, and all other questions shall be decided by a majority of the votes cast by stockholders entitled to vote thereon at a duly held meeting of stockholders at which a quorum is present.

Voting Rights. Each holder of common stock is entitled to one vote for each share held of record on all matters to be voted upon by stockholders. The common stock does not have cumulative voting rights.

Dividends. Subject to the rights, powers and preferences of any outstanding preferred stock, and except as provided by law or in our certificate of incorporation, dividends may be declared and paid or set aside for payment on the common stock out of legally available assets or funds when and as declared by the board of directors.

Liquidation, Dissolution and Winding Up. In the event of our liquidation or dissolution, the holders of our common stock are entitled to receive proportionately all assets available for distribution to stockholders after the payment of all debts and other liabilities and subject to the prior rights of any outstanding preferred stock. The rights, preferences and privileges of holders of our common stock are subject to and may be adversely affected by the rights of the holders of shares of any series of our preferred stock that we may designate and issue in the future.

Other Rights. Holders of the common stock have no right to:

• convert the stock into any other security;

• have the stock redeemed;

• purchase additional stock; or

• maintain their proportionate ownership interest.

Holders of shares of the common stock are not required to make additional capital contributions.

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Transfer Agent and Registrar. Computershare Trust Company, N.A. is transfer agent and registrar for the common stock.

Exchange Listing. Our common stock is listed on the Nasdaq Global Market under the symbol “TRVI.”

Preferred Stock

We are authorized to issue “blank check” preferred stock, which may be issued in one or more series upon authorization of our board of directors. Our board of directors is authorized to fix the designations, powers, preferences and the relative, participating, optional or other special rights and any qualifications, limitations and restrictions of the shares of each series of preferred stock. The authorized shares of our preferred stock are available for issuance without further action by our stockholders, unless such action is required by applicable law or the rules of any stock exchange on which our securities may be listed. If the approval of our stockholders is not required for the issuance of shares of our preferred stock, our board may determine not to seek stockholder approval.

Provisions of Our Certificate of Incorporation and By-laws and Delaware Law That May Have Anti-Takeover Effects

Board of Directors. Our certificate of incorporation and by-laws provide for a board of directors divided as nearly equally as possible into three classes. Each class is elected to a term expiring at the annual meeting of stockholders held in the third year following the year of such election. The number of directors comprising our board of directors is fixed from time to time by the board of directors.

Removal of Directors by Stockholders. Delaware law provides that members of our board of directors may only be removed for cause by a vote of the holders of 75% of the outstanding shares entitled to vote on the election of the directors.

Stockholder Nomination of Directors. Our by-laws provide that a stockholder must notify us in writing of any stockholder nomination of a director not more than 120 days and not less than the 90 days prior to the first anniversary of the preceding year’s annual meeting; provided, that if the date of the annual meeting is advanced or delayed by more than 30 days from such anniversary date, notice by the stockholder to be timely must be so delivered not earlier than the 120^th day prior to the date of such annual meeting and not later than the close of business on the later of (x) the 90^th day prior to the date of such meeting and (y) the 10^th day following the day on which notice of the date of such annual meeting was mailed or public disclosure of the date of such annual meeting was made, whichever occurs first.

No Action By Written Consent. Our certificate of incorporation provides that our stockholders may not act by written consent and may only act at duly called meetings of stockholders.

Delaware Law. We are subject to Section 203 of the Delaware General Corporation Law, or the DGCL. Subject to certain exceptions, Section 203 prevents a publicly held Delaware corporation from engaging in a “business combination” with any “interested stockholder” for three years following the date that the person became an interested stockholder, unless either the interested stockholder attained such status with the approval of our board of directors, the business combination is approved by our board of directors and stockholders in a prescribed manner or the interested stockholder acquired at least 85% of our outstanding voting stock in the transaction in which it became an interested stockholder. A “business combination” includes, among other things, a merger or consolidation involving us and the “interested stockholder” and the sale of more than 10% of our assets. In general, an “interested stockholder” is any entity or person beneficially owning 15% or more of our outstanding voting stock and any entity or person affiliated with or controlling or controlled by such entity or person.

Exclusive Forum Selection. Our certificate of incorporation provides that, unless we consent in writing to the selection of an alternative forum, the Court of Chancery of the State of Delaware (or, if the Court of Chancery of

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the State of Delaware does not have jurisdiction, the federal district court for the District of Delaware) shall be the sole and exclusive forum for (1) any derivative action or proceeding brought on behalf of our company, (2) any action asserting a claim of breach of a fiduciary duty owed by any of our directors, officers, other employees or stockholders to our company or our stockholders, (3) any action asserting a claim arising pursuant to any provision of the DGCL or as to which the DGCL confers jurisdiction on the Court of Chancery of the State of Delaware or (4) any action asserting a claim arising pursuant to any provision of our certificate of incorporation or by-laws (in each case, as they may be amended from time to time) or governed by the internal affairs doctrine. Our certificate of incorporation further provides that, unless we consent in writing to the selection of an alternative forum, the federal district courts of the United States of America shall, to the fullest extent permitted by law, be the sole and exclusive forum for the resolution of any complaint asserting a cause of action arising under the Securities Act. Neither of these choice of forum provisions would affect suits brought to enforce any liability or duty created by the Exchange Act or the rules and regulations thereunder, jurisdiction over which is exclusively vested by statute in the United States federal courts, or any other claim for which United States federal courts have exclusive jurisdiction. Although our certificate of incorporation contains the choice of forum provisions described above, it is possible that a court could rule that such provisions are inapplicable for a particular claim or action.

Registration Rights

We are party to a second amended and restated investors’ rights agreement, which we refer to as the investors’ rights agreement, under which holders of a total of 10,325,257 shares of our common stock have the right to require us to register these shares under the Securities Act under specified circumstances. We refer to the shares with these registration rights as registrable securities. After registration pursuant to these rights, the registrable securities will become freely tradable without restriction under the Securities Act. In addition, in connection with

a private placement to New Enterprise Associates, or NEA, in May 2019, we granted NEA the right to require us to register under the Securities Act under specified circumstances the shares to NEA in such private placement, and upon such registration, such shares would become freely tradable without restriction under the Securities Act.

Demand and Form S-3 Registration Rights. Subject to specified limitations and conditions set forth in the investors’ rights agreement, at any time, the holders of at least a majority of the then outstanding registrable securities may demand that we register registrable securities then outstanding under the Securities Act for purposes of a public offering having an aggregate offering price to the public of not less than $10.0 million, net of certain expenses, underwriting discounts and selling commissions. We are not obligated to file a registration statement pursuant to this provision on more than two occasions. In addition, subject to specified limitations and conditions set forth in the investors’ rights agreement, at any time when we are eligible to file a registration statement on Form S-3, holders of the registrable securities then outstanding may request that we register their registrable securities on Form S-3 for purposes of a public offering for which the reasonably anticipated aggregate offering price to the public, net of certain expenses, underwriting discounts and selling commissions, would exceed $1.0 million. We are not obligated to file a registration statement pursuant to this provision on more than two occasions in any 12-month period.

Incidental Registration Rights. If we propose to register for our own account or for the account of our other stockholders any of our common stock under the Securities Act, the holders of registrable securities will be entitled to notice of the registration and, subject to specified exceptions, have the right to require us to register all or a portion of the registrable securities then held by them in that registration. In the event that any registration in which the holders of registrable securities participate pursuant to our investors’ rights agreement is an underwritten public offering, we have agreed to enter into an underwriting agreement in usual and customary form and use our commercially reasonable efforts to facilitate such offering.

Expenses and Indemnification. Pursuant to the investors’ rights agreement, we are required to pay all registration expenses, including all registration and filing fees, exchange listing fees, printing expenses, fees and expenses of

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one counsel selected by the selling stockholders to represent the selling stockholders, state Blue Sky fees and expenses, and the expense of any special audits incident to or required by any such registration, but excluding underwriting discounts, selling commissions, stock transfer taxes and the fees and expenses of the selling stockholders’ own counsel (other than the counsel selected to represent all selling stockholders). The investors’ rights agreement contains customary cross-indemnification provisions, pursuant to which we are obligated to indemnify the selling stockholders in the event of material misstatements or alleged material misstatements or material omissions or alleged material omissions in the registration statement attributable to us, or any violation or alleged violation, whether by action or inaction, by us under the Securities Act; the Exchange Act; any state securities or Blue Sky law or any rule or regulation promulgated under the Securities Act, the Exchange Act or any state securities or Blue Sky law in connection with such registration statement or the qualification or compliance of the offering, and they are obligated to indemnify us for material misstatements or omissions in the registration statement attributable to them.

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PLAN OF DISTRIBUTION

We have entered into a Sales Agreement with SVB Leerink LLC, or SVB Leerink, under which we may issue and sell up to $12.0 million of our common stock from time to time through SVB Leerink as our sales agent. Sales of our common stock, if any, will be made by any method that is deemed to be an “at the market offering” as defined in Rule 415 under the Securities Act, including sales made directly on or through the Nasdaq Global Market, on or through any other existing trading market for the common stock or to or through a market maker.

SVB Leerink will offer our common stock subject to the terms and conditions of the Sales Agreement on a daily basis or as otherwise agreed upon by us and SVB Leerink. We will designate the maximum number or amount of common stock to be sold through SVB Leerink on a daily basis or otherwise determine such maximum number or amount together with SVB Leerink. Subject to the terms and conditions of the Sales Agreement, SVB Leerink will use commercially reasonable efforts consistent with its normal trading and sales practices and applicable state and federal laws, rules and regulations and the rules of The Nasdaq Stock Market LLC to sell on our behalf all of the common stock requested to be sold by us. We may instruct SVB Leerink not to sell common stock if the sales cannot be effected at or above a minimum price designated by us in any such instruction. SVB Leerink or we may suspend the offering of our common stock being made through SVB Leerink under the Sales Agreement upon proper notice to the other party. SVB Leerink and we each have the right, by giving written notice as specified in the Sales Agreement, to terminate the Sales Agreement in each party’s sole discretion at any time. The offering of our common stock pursuant to the Sales Agreement will otherwise terminate upon the termination of the Sales Agreement as provided therein.

The compensation payable to SVB Leerink as sales agent will be an amount equal to 3.0% of the gross proceeds of any shares of common stock sold through it pursuant to the Sales Agreement. We have also agreed to reimburse SVB Leerink for actual outside legal expenses incurred by SVB Leerink in connection with this offering, including SVB Leerink’s counsel fees in an amount up to $50,000 in connection with the filing of this prospectus, plus an additional amount of up to $15,000 in connection with determining our compliance with the rules and regulations of the Financial Industry Regulatory Authority, Inc., or FINRA. We have also agreed to reimburse SVB Leerink for outside legal expenses in an amount up to $15,000 for each fiscal quarter thereafter during or with respect to which SVB Leerink conducts bring-down due diligence. In accordance with FINRA Rule 5110, these reimbursed fees and expenses are deemed sales compensation to SVB Leerink in connection with this offering. We estimate that the total expenses of the offering payable by us, excluding commissions payable to SVB Leerink under the Sales Agreement, will be approximately $250,000.

The remaining sales proceeds, after deducting any expenses payable by us and any transaction fees imposed by any governmental, regulatory or self-regulatory organization in connection with the sales of our common stock, will equal our net proceeds for the sale of such common stock.

SVB Leerink will provide written confirmation to us no later than the next succeeding trading day on the Nasdaq Global Market after each day on which common stock is sold through it as sales agent under the Sales Agreement. Each confirmation will include the number or amount of shares sold through it as sales agent on that day, the volume-weighted average price of the shares sold and the net proceeds to us from such sales.

We will report at least quarterly the number of shares of common stock sold through SVB Leerink under the Sales Agreement, the net proceeds to us and the compensation paid by us to SVB Leerink in connection with the sales of common stock during the relevant period.

Settlement for sales of common stock will occur, unless the parties agree otherwise, on the second trading day following the date on which any sales were made in return for payment of the net proceeds to us. There is no arrangement for funds to be received in an escrow, trust or similar arrangement.

In connection with the sale of the common stock on our behalf pursuant to the Sales Agreement, SVB Leerink will be deemed to be an “underwriter” within the meaning of the Securities Act and the compensation paid to SVB Leerink will be deemed to be underwriting commissions or discounts. We have agreed in the Sales

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Agreement to provide indemnification and contribution to SVB Leerink with respect to certain liabilities, including liabilities under the Securities Act and the Exchange Act. As sales agent, SVB Leerink will not engage in any transactions that stabilize our common stock.

Our common stock is listed on the Nasdaq Global Market and trades under the symbol “TRVI.” The transfer agent of our common stock is Computershare Trust Company, N.A.

SVB Leerink and/or its affiliates have provided, and may in the future provide, various investment banking, lending and other financial services for us for which services they have received, and may in the future receive, customary fees.

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LEGAL MATTERS

The validity of the common stock being offered by this prospectus will be passed upon by Wilmer Cutler Pickering Hale and Dorr LLP, Boston, Massachusetts. Covington & Burling LLP, New York, New York, is counsel to SVB Leerink in connection with this offering.

EXPERTS

The consolidated financial statements of Trevi Therapeutics, Inc. appearing in Trevi Therapeutics, Inc.’s Annual Report (Form 10-K) for the years ended December 31, 2019 and 2018 have been audited by Ernst & Young LLP, independent registered public accounting firm, as set forth in their report thereon, included therein, and incorporated herein by reference. Such consolidated financial statements are incorporated herein by reference in reliance upon such report given on the authority of such firm as experts in accounting and auditing.

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WHERE YOU CAN FIND MORE INFORMATION

We file annual, quarterly and current reports, proxy statements and other information with the SEC. Our SEC filings are available to the public over the Internet at the SEC’s website at www.sec.gov. Copies of certain information filed by us with the SEC are also available on our website at www.trevitherapeutics.com. Our website is not a part of this prospectus and is not incorporated by reference in this prospectus. Our website address is included in this document as an inactive textual reference only.

This prospectus is part of a registration statement we filed with the SEC. This prospectus omits some information contained in the registration statement in accordance with SEC rules and regulations. You should review the information and exhibits in the registration statement for further information about us and our subsidiary and the securities we are offering. Statements in this prospectus concerning any document we filed as an exhibit to the registration statement or that we otherwise filed with the SEC are not intended to be comprehensive and are qualified by reference to these filings. You should review the complete document to evaluate these statements. You can obtain a copy of the registration statement from the SEC’s website.

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INFORMATION INCORPORATED BY REFERENCE

The SEC allows us to incorporate by reference into this prospectus much of the information we file with the SEC, which means that we can disclose important information to you by referring you to those publicly available documents. The information that we incorporate by reference is considered to be part of this prospectus. Because we are incorporating by reference future filings with the SEC, this prospectus is continually updated and those future filings may modify or supersede some of the information included or incorporated in this prospectus. This means that you must look at all of the SEC filings that we incorporate by reference to determine if any of the statements in this prospectus or in any document previously incorporated by reference have been modified or superseded. This prospectus incorporates by reference the documents listed below (File No. 001-38886) and any future filings we make with the SEC under Sections 13(a), 13(c), 14 or 15(d) of the Exchange Act (in each case, other than those documents or the portions of those documents not deemed to be filed), until the offering of the securities under the registration statement is terminated or completed:

• Annual Report on Form 10-K for the fiscal year ended December 31, 2019, filed on March 16, 2020, including the information specifically incorporated by reference into the Annual Report on Form 10-K from our definitive proxy statement for the 2020 Annual Meeting of Stockholders;

• Quarterly Report on Form 10-Q for the fiscal quarter ended March 31, 2020, filed on May 7, 2020;

• Current Reports on Form 8-K filed on January 6, 2020, February 18, 2020, June  17, 2020, and June 30, 2020; and

• The description of our common stock contained in our Registration Statement on Form 8-A filed on April 29, 2019, including any amendments or reports filed for the purpose of updating such description.

You may request a copy of these filings, at no cost, by writing or telephoning us at the following address or telephone number:

Trevi Therapeutics, Inc.

195 Church Street, 14th Floor

New Haven, Connecticut 06510

(203) 304-2499

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Up to $12,000,000

Common Stock

PROSPECTUS

SVB Leerink LLC

July 2, 2020