Exhibit 10.9

EVOKE PHARMA, INC.

NON-EMPLOYEE DIRECTOR COMPENSATION POLICY

Non-employee members of the board of directors (the “Board”) of Evoke Pharma, Inc. (the “Company”) shall be eligible to receive cash and equity compensation commencing on the date immediately preceding the first date upon which the Company’s common stock is listed upon notice of issuance as a national market security on an interdealer quotation system (the “Public Trading Date”), as set forth in this Non-Employee Director Compensation Policy (this “Policy”). The cash and equity compensation described in this Policy shall be paid or be made, as applicable, automatically and without further action of the Board, to each member of the Board who is not an employee of the Company or any parent or subsidiary of the Company (each, a “Non-Employee Director”) who may be eligible to receive such cash or equity compensation, unless such Non-Employee Director declines the receipt of such cash or equity compensation by written notice to the Company. This Policy shall remain in effect until it is revised or rescinded by further action of the Board. The terms and conditions of this Policy shall supersede any prior cash or equity compensation arrangements between the Company and its Non-Employee Directors.

1. Cash Compensation.

(a) Annual Retainers. Each Non-Employee Director shall be eligible to receive an annual retainer of $17,500 for service on the Board. In addition, a Non-Employee Director shall receive the following additional annual retainers, as applicable:

(i) Chairperson of the Board. A Non-Employee Director serving as Chairperson of the Board shall receive an additional annual retainer of $17,500 for such service.

(ii) Chairperson of the Audit Committee. A Non-Employee Director serving as Chairperson of the Audit Committee shall receive an additional annual retainer of $7,500 for such service.

(iii) Member of the Audit Committee. A Non-Employee Director serving as a member of the Audit Committee (other than the Chairperson) shall receive an additional annual retainer of $3,750 for such service.

(iv) Chairperson of the Compensation Committee. A Non-Employee Director serving as Chairperson of the Compensation Committee shall receive an additional annual retainer of $5,000 for such service.

(v) Member of the Compensation Committee. A Non-Employee Director serving as a member of the Compensation Committee (other than the Chairperson) shall receive an additional annual retainer of $2,500 for such service.

(vi) Chairperson of the Nominating and Corporate Governance Committee. A Non-Employee Director serving as Chairperson of the Nominating and Corporate Governance Committee shall receive an additional annual retainer of $3,500 for such service.

(vii) Member of the Nominating and Corporate Governance Committee. A Non-Employee Director serving as a member of the Nominating and Corporate Governance Committee (other than the Chairperson) shall receive an additional annual retainer of $1,750 for such service.

(b) Payment of Retainers. The annual retainers described in Section 1(a) shall be earned on a quarterly basis based on a calendar quarter and shall be paid by the Company in arrears not later than the fifth business day following the end of each calendar quarter. In the event a Non-Employee Director does not serve as a Non-Employee Director, or in the applicable positions described in Section 1(a), for an entire calendar quarter, the retainer paid to such Non-Employee Director shall be prorated for the portion of such calendar quarter actually served as a Non-Employee Director, or in such positions, as applicable.

2. Equity Compensation. Non-Employee Directors shall be granted the equity awards described below. The awards described below shall be granted under and shall be subject to the terms and provisions of the 2013 Equity Incentive Award Plan (the “Equity Plan”) and shall be granted subject to the execution and delivery of award agreements, including attached exhibits, in substantially the same forms previously approved by the Board, setting forth the vesting schedule applicable to such awards and such other terms as may be required by the Equity Plan.

(a) Initial Awards. A person who is serving as a Non-Employee Director on the date immediately preceding the Public Trading Date shall be eligible to receive a stock option to purchase 18,000 shares of the Company’s common stock on such date. In addition, a person who is initially elected or appointed to the Board following the Public Trading Date, and who is a Non-Employee Director at the time of such initial election or appointment, shall be eligible to receive a stock option to purchase 18,000 shares of the Company’s common stock on the date of such initial election or appointment. The awards described in this Section 2(a) shall be referred to as “Initial Awards.” No Non-Employee Director shall be granted more than one Initial Award.

(b) Subsequent Awards. A person who is a Non-Employee Director immediately following each annual meeting of the Company’s stockholders after the Public Trading Date and who will continue to serve as a Non-Employee Director immediately following such annual meeting shall be automatically granted an option to purchase 9,000 shares of the Company’s common stock on the date of each such annual meeting. The awards described in this Section 2(b) shall be referred to as “Subsequent Awards.” For the avoidance of doubt, a Non-Employee Director elected for the first time to the Board at an annual meeting of the Company’s stockholders shall only receive an Initial Award in connection with such election, and shall not receive any Subsequent Award on the date of such meeting as well.

(c) Termination of Employment of Employee Directors. Members of the Board who are employees of the Company or any parent or subsidiary of the Company who subsequently terminate their employment with the Company and any parent or subsidiary of the Company and remain on the Board will not receive an Initial Award pursuant to Section 2(a) above, but to the extent that they are otherwise eligible, will be eligible to receive, after termination from employment with the Company and any parent or subsidiary of the Company, Subsequent Awards as described in Section 2(b) above.

(d) Terms of Awards Granted to Non-Employee Directors.

(i) Purchase Price. The per share exercise price of each option granted to a Non-Employee Director shall equal 100% of the Fair Market Value (as defined in the Equity Plan) of a share of common stock on the date the option is granted; provided, however, that the per share exercise price of each Initial Award granted to a Non-Employee Director on the date immediately preceding the Public Trading Date shall equal the initial public offering price per share of the Company’s common stock.

(ii) Vesting. Each Initial Award shall vest and become exercisable in three equal annual installments over the three year period following the date of grant, subject to the Non-Employee Director continuing in service on the Board through each such vesting date. Each Subsequent Award shall vest and/or become exercisable on the one-year anniversary of the date of grant, subject to the Non-Employee Director continuing in service on the Board through each such vesting date. All of a Non-Employee Director’s Initial Awards and Subsequent Awards shall vest in full upon the occurrence of a Change in Control (as defined in the Equity Plan).

(iii) Term. The term of each stock option granted to a Non-Employee Director shall be ten years from the date the option is granted. Upon a Non-Employee Director’s termination of membership on the Board for any reason, his or her stock options granted under this Policy shall remain exercisable for twelve months following his or her termination of membership on the Board (or such longer period as the Board may determine in its discretion on or after the date of grant of such stock options).