Exhibit 23.1

Consent of Independent Registered Public Accounting Firm

We consent to the incorporation by reference in the following Registration Statements:

1. Registration Statement (Form S-3 Nos. 333-210614 and 333-221479) of Kura Oncology, Inc., and

2. Registration Statement (Form S-8 Nos. 333-210260 and 333-216683) pertaining to the Amended and Restated 2014 Equity Incentive Plan and the 2015 Employee Stock Purchase Plan of Kura Oncology, Inc.;

of our report dated March 12, 2018, with respect to the financial statements of Kura Oncology, Inc., included in this Annual Report (Form 10-K) of Kura Oncology, Inc. for the year ended December 31, 2017.

/s/ Ernst & Young LLP

San Diego, California

March 12, 2018