UNITED STATES

SECURITIES AND EXCHANGE COMMISSION

WASHINGTON, D.C. 20549

SCHEDULE 13D

Under the Securities Exchange Act of 1934

(Amendment No.     )*

Corvus Pharmaceuticals, Inc.

(Name of Issuer)

Common Stock, par value $0.0001 per share

(Title of Class of Securities)

221015 10 0

(CUSIP Number)

Thomas Dyrberg

Novo A/S

Tuborg Havnevej 19

Hellerup, Denmark DK-2900

+45 3527 6592

Copy to:

B. Shayne Kennedy, Esq.

Latham & Watkins LLP

650 Town Center Drive, 20^th Floor

Costa Mesa, CA 92626

Telephone: (714) 540-1235

(Name, Address and Telephone Number of Person Authorized to Receive Notices and Communications)

March 29, 2016

(Date of Event which Requires Filing of this Statement)

If the filing person has previously filed a statement on Schedule 13G to report the acquisition which is subject of this Schedule 13D, and is filing this statement because of Rule 13d-1(e), 13d-1(f) or 13d-1(g), check the following box.  ¨

Note: Schedules filed in paper format shall include a signed original and five copies of the schedule, including all exhibits. See Rule 13d-7(b) for other parties to whom copies are to be sent.

The information required on the remainder of this cover page shall not be deemed to be “filed” for the purpose of Section 18 of the Securities Exchange Act of 1934 (the “Act”) or otherwise subject to the liabilities of that section of the Act but shall be subject to all other provisions of the Act (however, see the Notes).

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This Schedule 13D relates to the shares of common stock, par value $0.001 per share (the “Common Stock”), of Corvus Pharmaceuticals, Inc., a Delaware corporation (the “Issuer”). The Issuer’s principal executive office is located at 863 Mitten Road, Suite 102, Burlingame, California 94010.

The name of each director and executive officer of both Novo A/S and the Foundation is set forth on Schedule I to this Schedule 13D.

The residence or business address of each director and executive officer of both Novo A/S and the Foundation is set forth on Schedule I to this Schedule 13D.

The Foundation is a Danish self-governing and profit-making foundation, whose objectives are to provide a stable basis for commercial and research activities undertaken by the group of Novo companies and to support scientific, humanitarian and social purposes through grants.

Prior to the Issuer’s initial public offering (the “IPO”), the Reporting Person held the following securities of the Issuer:

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The purchase price of the Preferred Stock was paid by Novo A/S from its working capital.

On March 29, 2016, the closing date of the IPO:

The acquisitions of Issuer securities made by Novo A/S, as described in this Schedule 13D, were for investment purposes. Novo A/S intends to review its investments in the Issuer on a continuing basis and any actions Novo A/S might undertake will be dependent upon its review of numerous factors from time to time, including, but not limited to: an ongoing evaluation of the Issuer’s business, financial condition, operations and prospects; price levels of the Issuer’s securities; general market, industry and economic conditions; the relative attractiveness of alternative business and investment opportunities; and other future developments. Novo A/S may, at any time and from time to time, acquire additional securities of the Issuer, or retain or sell all or a portion of the securities of the Issuer then held, in the open market or in privately negotiated transactions. Other than as described herein, Novo A/S currently does not have any plans or proposals that relate to, or would result in, any of the matters listed in Items 4(a)–(j) of Schedule 13D, although, depending on the factors discussed herein, Novo A/S may change its purpose or formulate different plans or proposals with respect thereto at any time. Peter Moldt, Ph.D., a member of the board of directors of the Issuer, is employed as a Partner of Novo Ventures (US) Inc., a company that provides consultancy services to Novo A/S. Dr. Moldt is not deemed a beneficial owner of, and does not have a reportable pecuniary interest in, the Novo Shares (as defined below).

(a) Novo A/S beneficially owns 3,154,046 shares (the “Novo Shares”) of Common Stock representing approximately 15.5% of the Issuer’s outstanding Common Stock, based upon 20,406,356 shares of the Issuer’s Common Stock outstanding as of the Issuer’s initial public offering as reported in the Issuer’s prospectus (Form 424B4) filed with the Securities and Exchange Commission on March 24, 2016.

(b) Novo A/S is a Danish limited liability company wholly owned by the Novo Nordisk Foundation. Novo A/S, through its Board of Directors (the “Novo Board”), has the sole power to vote and dispose of the Novo Shares. The Novo Board, currently comprised of Sten Scheibye, Goran Ando, Jeppe Christiansen, Steen Riisgaard and Per Wold-Olsen, may exercise voting and dispositive control over the Novo Shares only with the support of a majority of the Novo Board. As such, no individual member of the Novo Board is deemed to hold any beneficial ownership or reportable pecuniary interest in the Novo Shares. Peter Moldt, Ph.D., a member of the board of directors of the Issuer, is employed as a Partner of Novo Ventures (US) Inc., a company that provides consultancy services to Novo A/S. Dr. Moldt is not deemed a beneficial owner of, and does not have a reportable pecuniary interest in, the Novo Shares. Except as described in this Schedule 13D, neither the Foundation nor any person listed on Schedule I has the power to direct the vote as to, or the disposition of the Novo Shares.

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(c) Except as set forth in Item 3 of this Schedule 13D, Novo A/S has not effected any transactions in the Issuer’s Common Stock within the past 60 days and neither the Foundation nor any person listed on Schedule I has effected any transactions in the Issuer’s Common Stock within the past 60 days.

(d) Novo A/S does not know of any other person having the right to receive or the power to direct the receipt of dividends from, or the proceeds from the sale of the Issuer’s Common Stock held in the name of the Novo A/S and reported herein.

(e) Not applicable.

Amended and Restated Investors’ Rights Agreement

The Issuer, Novo A/S and certain other holders of the Issuer’s securities are party to that certain Amended and Restated Investors’ Rights Agreement dated as of September 16, 2015 to become effective upon the closing of the IPO (the “Investors’ Rights Agreement”). The Investors’ Rights Agreement grants to Novo A/S and the other parties thereto certain rights that include demand registration rights, piggyback registration rights and Form S-3 registration rights as more fully described in such agreement which will expire, with respect to any particular stockholder, upon the earlier of four years after the consummation of the IPO or when such stockholder can immediately sell all of its shares under Rule 144 of the Securities Act of 1933, as amended (the “Securities Act”), during any 90 day period (and without the requirement for the Company to be in compliance with the current public information required under Section c(1) of Rule 144 of the Securities Act).

Lock-Up Agreement

In connection with the Issuer’s initial public offering, Novo A/S entered into a letter agreement (the “Lock-Up Agreement”) with the Issuer and the Underwriters, pursuant to which Novo A/S agreed that, during the “Lock-Up Period” as defined below and subject to certain limited exceptions specified in the Lock-Up Agreement, Novo A/S will not (1) offer, pledge, sell, contract to sell, sell any option or contract to purchase, purchase any option or contract to sell, grant any option, right or warrant to purchase, lend, or otherwise transfer or dispose of, directly or indirectly, any shares of Common Stock beneficially owned or any securities convertible into or exercisable or exchangeable for Common Stock; (2) enter into any swap or other arrangement that transfers to another, in whole or in part, any of the economic consequences of ownership of Common Stock; or (3) publicly disclose the intention to make any such offer, sale, pledge or disposition of shares of Common Stock. In addition, Novo A/S has agreed in the Lock-Up Agreement that, without the prior written consent of the Underwriters, it will not, during the Lock-Up Period, make any demand for or exercise any right with respect to, the registration of any shares of the Issuer’s capital stock. The “Lock-Up Period” is defined in the Lock-Up Agreement as the period ending 180 days after the date of the final prospectus used to sell Common Stock in the Issuer’s initial public offering. The Lock-Up Agreement automatically terminates and shall be of no further force or effect following the expiration of the Lock-Up Period.

The descriptions contained in this Statement on Schedule 13D of the Investors’ Rights Agreement and the Lock-Up Agreement are summaries only and are qualified in their entireties by the actual terms of each such agreement, which are incorporated herein by this reference. See Item 7 “Material to be Filed as Exhibits.”

Except for the Investors’ Rights Agreement and the Lock-Up Agreement, neither Novo A/S, the Foundation, nor any person named in Schedule I has entered into any contracts, arrangements, understandings or relationships with respect to securities of the Issuer.

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Exhibit A – Amended and Restated Investor Rights Agreement, dated as of September 16, 2015 (incorporated by reference to Exhibit 10.1 of Form S-1 Registration Statement of the Issuer filed January 4, 2016 (File No. 333-208850)).

Exhibit B – Form of Lock-Up Agreement.

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SIGNATURE

After reasonable inquiry and to the best of my knowledge and belief, I certify that the information set forth in this statement is true, complete and correct.

Signature Page to Schedule 13D

Schedule I

Information regarding each director and executive officer of both Novo A/S and the Novo Nordisk Foundation is set forth below.