Exhibit 31.4

Certification of Chief Financial Officer

Pursuant to Section 302 of the Sarbanes-Oxley Act of 2002

I, Jean-Marc Bellemin, Chief Financial Officer of Gritstone Oncology, Inc., certify that:

1. I have reviewed this Amendment No. 1 to the Annual Report on Form 10-K/A of Gritstone Oncology, Inc.; and

2. Based on my knowledge, this report does not contain any untrue statement of a material fact or omit to state a material fact necessary to make the statements made, in light of the circumstances under which such statements were made, not misleading with respect to the period covered by this report.

Date: April 18, 2019	By:	/s/ Jean-Marc Bellemin
		Jean-Marc Bellemin
		Chief Financial Officer (Principal Financial Officer)