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

    <schemaVersion>X0508</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2023-08-22</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001618673</issuerCik>
        <issuerName>Performance Food Group Co</issuerName>
        <issuerTradingSymbol>PFGC</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001045958</rptOwnerCik>
            <rptOwnerName>HOLM GEORGE L</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>12500 WEST CREEK PARKWAY</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>RICHMOND</rptOwnerCity>
            <rptOwnerState>VA</rptOwnerState>
            <rptOwnerZipCode>23238</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>See Remarks</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <aff10b5One>0</aff10b5One>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2023-08-22</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
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            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>104809</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1494835</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
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        <nonDerivativeTransaction>
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                <value>Common Stock</value>
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                    <value>47269</value>
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                    <value>60.99</value>
                </transactionPricePerShare>
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                </transactionAcquiredDisposedCode>
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            <securityTitle>
                <value>Common Stock</value>
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            <transactionDate>
                <value>2023-08-23</value>
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            <deemedExecutionDate></deemedExecutionDate>
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                <transactionFormType>4</transactionFormType>
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                </transactionShares>
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    <footnotes>
        <footnote id="F1">Represents a grant of performance-based restricted stock under the 2015 Omnibus Incentive Plan that vested on the date the Human Capital and Compensation Committee of the Company certified the achievement of the applicable performance targets based on the extent to which the applicable performance goals, which are based on relative total shareholder return, were attained for the performance period of June 28, 2020 to July 1, 2023.</footnote>
        <footnote id="F2">Represents a grant of restricted stock that vests in three equal annual installments beginning on August 23, 2024.</footnote>
    </footnotes>

    <remarks>Title: Chairman of the Board of Directors and Chief Executive Officer</remarks>

    <ownerSignature>
        <signatureName>/s/ A. Brent King, as Attorney in Fact</signatureName>
        <signatureDate>2023-08-24</signatureDate>
    </ownerSignature>
</ownershipDocument>
