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

    <schemaVersion>X0206</schemaVersion>

    <documentType>3</documentType>

    <periodOfReport>2022-01-11</periodOfReport>

    <noSecuritiesOwned>1</noSecuritiesOwned>

    <issuer>
        <issuerCik>0001848948</issuerCik>
        <issuerName>10X Capital Venture Acquisition Corp. III</issuerName>
        <issuerTradingSymbol>VCXB</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001828663</rptOwnerCik>
            <rptOwnerName>Weisburd David</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>10X CAPITAL VENTURE ACQUISITION CORP.</rptOwnerStreet1>
            <rptOwnerStreet2>III 1 WORLD TRADE CENTER, 85TH FLOOR</rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10007</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>COO &amp; Head of Origination</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <footnotes></footnotes>

    <remarks>See Exhibit 24.1 - Power of Attorney.</remarks>

    <ownerSignature>
        <signatureName>/s/ Joanna Heinz, Attorney-in-Fact</signatureName>
        <signatureDate>2022-01-11</signatureDate>
    </ownerSignature>
</ownershipDocument>
