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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2018-01-31</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000837465</issuerCik>
        <issuerName>CALLAWAY GOLF CO</issuerName>
        <issuerTradingSymbol>ELY</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001696849</rptOwnerCik>
            <rptOwnerName>Arnett Richard H.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>2180 RUTHERFORD ROAD</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>CARLSBAD</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>92008</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>SVP, Glb. Mktg. &amp; Pres., OGIO</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Performance Stock Unit</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F1"/>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2018-01-31</value>
                <footnoteId id="F2"/>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>6585</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F2"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F2"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>6585</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>17560</value>
                    <footnoteId id="F3"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
                <value>Performance Stock Unit</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F1"/>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2018-01-31</value>
                <footnoteId id="F4"/>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>10952</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F4"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F4"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>10952</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>10951</value>
                    <footnoteId id="F5"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">Each Performance Stock Unit represents a contingent right to receive one share of common stock, subject to the achievement of applicable performance criteria.</footnote>
        <footnote id="F2">The Reporting Person was granted a total of 21,950 target Performance Stock Units (&quot;PSUs&quot;) on February 8, 2016, the vesting of which are subject to the achievement of certain performance criteria.  The Reporting Person may be eligible to vest in up to 200% of such target PSUs during the three year period ending December 31, 2018.  On January 31, 2018, the Compensation and Management Succession Committee of the Board of Directors determined that 80% of the target award was deemed to be achieved under the terms of the PSUs as a result of the Company's performance during 2017. As a result, 6,585 of the PSUs converted to time-based units that will vest on the third anniversary of the grant date provided the recipient remains employed by Callaway Golf Company through such date.  The Reporting Person remains eligible to vest in the remaining PSUs subject to the original award subject to the achievement of certain performance criteria.</footnote>
        <footnote id="F3">Represents only that portion of the PSUs originally granted on February 8, 2016 for which the performance criteria was achieved on January 18, 2017 and January 31, 2018, and does not include the other PSUs originally granted on such date or any other PSUs with different grant dates or vesting terms.</footnote>
        <footnote id="F4">The Reporting Person was granted a total of 21,903 target Performance Stock Units (&quot;PSUs&quot;) on February 6, 2017, the vesting of which are subject to the achievement of certain performance criteria. The Reporting Person may be eligible to vest in up to 200% of such target PSUs during the three year period ending December 31, 2019. On January 31, 2018, the Compensation and Management Succession Committee of the Board of Directors determined that 50% of the target award was deemed to be achieved under the terms of the PSUs as a result of the Company's performance during 2017. As a result, 10,952 of the PSUs converted to time-based units that will vest on the third anniversary of the grant date provided the recipient remains employed by Callaway Golf Company through such date. The Reporting Person remains eligible to vest in the remaining PSUs subject to the original award subject to the achievement of certain performance criteria.</footnote>
        <footnote id="F5">Represents only that portion of the PSUs originally granted on February 6, 2017 for which the performance criteria was achieved on January 31, 2018, and does not include the other PSUs originally granted on such date or any other PSUs with different grant dates or vesting terms.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Peter C. Bartolino Attorney-in-Fact for Richard H. Arnett under a Limited Power of Attorney dated January 30, 2018.</signatureName>
        <signatureDate>2018-02-01</signatureDate>
    </ownerSignature>
</ownershipDocument>
