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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2023-02-02</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001374539</rptOwnerCik>
            <rptOwnerName>Allen Andrew R</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>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>President and CEO</officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2023-02-02</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>738550</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>856750</value>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1449275</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See footnote</value>
                    <footnoteId id="F3"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">Represents Restricted Stock Units (&quot;RSUs&quot;) 499,241 of which vest semi-annually over four years and 239,309 of which vest annually over two years from February 1, 2023, in each case, subject to the Reporting Person's continuous service to the Issuer on each such date.  Each RSU represents a contingent right to receive one share of common stock of the Issuer.</footnote>
        <footnote id="F2">Includes 738,550 RSUs which are subject to vesting.</footnote>
        <footnote id="F3">The shares are held in the name of the Reporting Person's revocable trust of which the Reporting Person is a co-trustee. The Reporting person disclaims beneficial ownership of the shares except to the extent of his pecuniary interest therein.</footnote>
    </footnotes>

    <ownerSignature>
        <signatureName>/s/ Vassiliki (Celia) Economides, Attorney-in-Fact for Andrew R. Allen</signatureName>
        <signatureDate>2023-02-06</signatureDate>
    </ownerSignature>
</ownershipDocument>
