Exhibit 23.1

CONSENT OF INDEPENDENT REGISTERED PUBLIC ACCOUNTING FIRM

We consent to the incorporation by reference in the Registration Statement (Form S-8 No. 333-227665) pertaining to the 2015 Equity Incentive Plan, the 2018 Incentive Award Plan, and 2018 Employee Stock Purchase Plan of Gritstone Oncology, Inc. of our report dated March 28, 2019, with respect to the financial statements of Gritstone Oncology, Inc. included in this Annual Report (Form 10-K) for the year ended December 31, 2018.

/s/ Ernst & Young LLP

Redwood City, California

March 28, 2019