Exhibit 23.1

Consent of Independent Registered Public Accounting Firm

We consent to the incorporation by reference in the Registration Statements (Form S-8 No. 333-191700 and No. 333-194820 and Form S-3 No. 333-200067) of Five Prime Therapeutics Inc. of our report dated March 18, 2015, with respect to the financial statements Five Prime Therapeutics, Inc. included in its Annual Report (Form 10-K) for the year ended December 31, 2014, filed with the Securities and Exchange Commission.

/s/ Ernst & Young LLP

San Jose, California

March 18, 2015