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. 333-228172 and 333-232947) of Kura Oncology, Inc.,

2. Registration Statement (Form S-8 Nos. 333-203504 and 333-210260) pertaining to the Amended and Restated 2014 Equity Incentive Plan and the 2015 Employee Stock Purchase Plan of Kura Oncology, Inc., and

3. Registration Statement (Form S-8 Nos. 333-216683, 333-223591 and 333-230075) pertaining to the Amended and Restated 2014 Equity Incentive Plan of Kura Oncology, Inc.;

of our reports dated February 25, 2020, with respect to the financial statements of Kura Oncology, Inc. and the effectiveness of internal control over financial reporting of Kura Oncology, Inc. included in this Annual Report (Form 10-K) of Kura Oncology, Inc. for the year ended December 31, 2019.

/s/ Ernst & Young LLP

San Diego, California

February 25, 2020