AMENDMENT TO EMPLOYMENT AGREEMENT

Exhibit 10.20

AMENDMENT TO

EMPLOYMENT AGREEMENT

THIS AMENDMENT TO EMPLOYMENT AGREEMENT (this “Amendment”) is entered into effective as of July 2, 2013, by and between Gary Burgess, M.B., Ch.B. M.Med. (“Employee”) and Conatus Pharmaceuticals Inc., a Delaware corporation (the “Company”).

WHEREAS, the Company and Employee are parties to that certain Employment Agreement dated as of November 1, 2011 (the “Agreement”); and

WHEREAS, the Company and Employee desire to amend the Agreement on the terms and conditions set forth below.

NOW, THEREFORE, in consideration of the foregoing, and for other good and valuable consideration, the receipt and adequacy of which is hereby acknowledged, the Company and Employee hereby amend the Agreement as follows:

1. For purposes of the Agreement and this Amendment, the following terms shall have the following meanings:

“Stock Awards. “Stock Awards” shall mean all stock options, restricted stock and such other awards granted pursuant to the Company’s stock option and equity incentive award plans or agreements and any shares of stock issued upon exercise thereof.”

“Public Trading Date. “Public Trading Date” shall mean the first date upon which the Company’s common stock is listed (or approved for listing) upon notice of issuance on any securities exchange or designated (or approved for designation) upon notice of issuance as a national market security on an interdealer quotation system.”

2. The first sentence of Section 4(a) of the Agreement is hereby amended to read as follows:

“The Company shall pay to Employee a base salary of USD $288,400.00 per year, payable in accordance with the Company’s usual pay practices (and in any event no less frequently than monthly).”

3. The second sentence of Section 4(b) of the Agreement is hereby amended to read as follows:

“Upon full attainment of the aforementioned criteria, as determined by the Board or its designee, the Annual Bonus will be equal to thirty-five percent (35%) of Employee’s then-current base salary actually paid for such fiscal year.”

4. The Agreement is hereby amended to include Section 4(g), which reads as follows:

“(g) Acceleration of Vesting of Stock Awards.

(i) With respect to Stock Awards granted to Employee on or after the Public Trading Date, (A) the vesting and/or exercisability of fifty percent (50%) of the then-unvested and outstanding portion of such Stock Awards shall be automatically accelerated on the date of a Change of Control, and (B) the remaining fifty percent (50%) of the then-unvested and outstanding portion of such Stock Awards shall vest and/or become exercisable on the first to occur of (1) the first anniversary of the Change of Control or (2) the date of Employee’s termination of employment by the Company without Cause or by Employee for Good Reason.

(ii) With respect to Stock Awards granted to Employee on or after the Public Trading Date, subject to Section 5(c), if Employee’s employment is terminated by the Company without Cause or by Employee for Good Reason, the vesting and/or exercisability of each of Employee’s outstanding Stock Awards shall be automatically accelerated on the date of termination as to the number of Stock Awards that would vest over the Severance Period (as defined below) had Employee remained continuously employed by the Company during such period.

(iii) The foregoing provisions are hereby deemed to be a part of each Stock Award and to supersede any less favorable provision in any agreement or plan regarding such Stock Award.”

5. The first sentence of Section 5(c) of the Agreement is hereby amended to read as follows:

“As a condition to Employee’s receipt of any post-termination benefits pursuant to Sections 4(g)(ii) and 5(a) above, on or prior to the sixtieth (60^th) day following the date of Employee’s termination of employment, Employee shall have executed and delivered a Release (the “Release”) in a form reasonably acceptable to the Company and any applicable revocation period applicable to such Release shall have expired.”

6. This Amendment shall be and is hereby incorporated in and forms a part of the Agreement. All other terms and provisions of the Agreement shall remain unchanged except as specifically modified herein. The Agreement, as amended by this Amendment, is hereby ratified and confirmed.

[Signature Page Follows]

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IN WITNESS WHEREOF, the Company and Employee have executed and delivered this Amendment on the date(s) set forth below.

[Signature Page to Amendment to Burgess Employment Agreement]