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

    <schemaVersion>X0206</schemaVersion>

    <documentType>3</documentType>

    <periodOfReport>2021-12-13</periodOfReport>

    <noSecuritiesOwned>1</noSecuritiesOwned>

    <issuer>
        <issuerCik>0001048911</issuerCik>
        <issuerName>FEDEX CORP</issuerName>
        <issuerTradingSymbol>FDX</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001686973</rptOwnerCik>
            <rptOwnerName>Perpall Frederick</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>THE BECK GROUP</rptOwnerStreet1>
            <rptOwnerStreet2>1601 ELM STREET, SUITE 2800</rptOwnerStreet2>
            <rptOwnerCity>DALLAS</rptOwnerCity>
            <rptOwnerState>TX</rptOwnerState>
            <rptOwnerZipCode>75201</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
        </reportingOwnerRelationship>
    </reportingOwner>

    <footnotes></footnotes>

    <ownerSignature>
        <signatureName>/s/ Frederick Perpall</signatureName>
        <signatureDate>2021-12-13</signatureDate>
    </ownerSignature>
</ownershipDocument>
