<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2021-03-08</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001656634</issuerCik>
        <issuerName>Gritstone Oncology, Inc.</issuerName>
        <issuerTradingSymbol>GRTS</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001782619</rptOwnerCik>
            <rptOwnerName>Yabannavar Vijay</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O GRITSTONE ONCOLOGY, INC.</rptOwnerStreet1>
            <rptOwnerStreet2>5959 HORTON STREET, SUITE 300</rptOwnerStreet2>
            <rptOwnerCity>EMERYVILLE</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>94608</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>See Remarks</officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable></nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Stock Option (Right to Buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>13.87</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2021-03-08</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>60000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <value>2021-04-08</value>
                <footnoteId id="F1"/>
            </exerciseDate>
            <expirationDate>
                <value>2031-03-07</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>60000</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>60000</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">One forty-eighth (1/48th) of the shares initially subject to the option will vest on each monthly anniversary measured from March 8, 2021 (the &quot;Vesting Commencement Date&quot;), so that 100% of the shares subject to the option will be fully vested and exercisable as of the fourth anniversary of the Vesting Commencement Date, subject to the Reporting Person's continued service through each vesting date.</footnote>
    </footnotes>

    <remarks>Executive Vice President, Manufacturing and Tech Ops</remarks>

    <ownerSignature>
        <signatureName>/s/ Rahsaan Thompson, Attorney-in-Fact for Vijay Yabannavar</signatureName>
        <signatureDate>2021-03-10</signatureDate>
    </ownerSignature>
</ownershipDocument>
