Exhibit 23.1

CONSENT OF INDEPENDENT REGISTERED PUBLIC ACCOUNTING FIRM

We consent to the reference to our firm under the caption “Experts” in the Registration Statement (Form S-1) and related Prospectus of Gritstone Oncology, Inc. for the registration of shares of its common stock and to the incorporation by reference therein of our report dated March 28, 2019, with respect to the financial statements of Gritstone Oncology, Inc. included in its Annual Report (Form 10-K) for the year ended December 31, 2018, filed with the Securities and Exchange Commission.

/s/ Ernst & Young LLP

Redwood City, California

April 22, 2019