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

    <schemaVersion>X0206</schemaVersion>

    <documentType>3</documentType>

    <periodOfReport>2015-10-01</periodOfReport>

    <noSecuritiesOwned>1</noSecuritiesOwned>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001276331</rptOwnerCik>
            <rptOwnerName>MELWANI PRAKASH</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O THE BLACKSTONE GROUP L.P.</rptOwnerStreet1>
            <rptOwnerStreet2>345 PARK AVENUE</rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10154</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <footnotes></footnotes>

    <remarks>Mr. Melwani, a Senior Managing Director of The Blackstone Group (&quot;Blackstone&quot;), is a member of the board of directors of Performance Food Group Company (the &quot;Issuer&quot;). Certain affiliates of Blackstone have filed separate Form 3 filings reporting securities of the Issuer that they may be deemed to beneficially own. Mr. Melwani disclaims beneficial ownership of any securities of the Issuer that may be deemed to be beneficially owned by affiliates of Blackstone.</remarks>

    <ownerSignature>
        <signatureName>/s/ Prakash A. Melwani</signatureName>
        <signatureDate>2015-10-01</signatureDate>
    </ownerSignature>
</ownershipDocument>
