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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2022-08-12</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001942990</rptOwnerCik>
            <rptOwnerName>Corey Lawrence</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O GRITSTONE BIO, INC.</rptOwnerStreet1>
            <rptOwnerStreet2>5959 HORTON STREET, SUITE 300</rptOwnerStreet2>
            <rptOwnerCity>EMERYVILLE</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>94608</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle></officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable></nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Stock Option (Right to Buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>4.10</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2022-08-12</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>38000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F1"/>
            </exerciseDate>
            <expirationDate>
                <value>2032-08-11</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>38000</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>38000</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">The Stock Option shall vest and become exercisable as to 1/36 of the total number of shares subject thereto on each monthly anniversary of the grant date such that the entire number of shares subject to the Stock Option are fully vested and exercisable on the third anniversary of the grant date, subject to Reporting Person's continuing service on the Issuer's board of directors through each vesting date.</footnote>
    </footnotes>

    <ownerSignature>
        <signatureName>/s/ Rahsaan Thompson, Attorney-in-Fact for Lawrence Corey</signatureName>
        <signatureDate>2022-08-16</signatureDate>
    </ownerSignature>
</ownershipDocument>
