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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4/A</documentType>

    <periodOfReport>2023-03-06</periodOfReport>

    <dateOfOriginalSubmission>2023-03-09</dateOfOriginalSubmission>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000798528</issuerCik>
        <issuerName>ODYSSEY MARINE EXPLORATION INC</issuerName>
        <issuerTradingSymbol>&quot;OMEX&quot;</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001231045</rptOwnerCik>
            <rptOwnerName>PIGNATELLI JAMES S</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>3715 RISING STAR LANE</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>PARK CITY</rptOwnerCity>
            <rptOwnerState>UT</rptOwnerState>
            <rptOwnerZipCode>84060</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Convertible debt</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>4.35</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2023-03-06</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>J</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionTotalValue>
                    <value>633002.00</value>
                    <footnoteId id="F2"/>
                </transactionTotalValue>
                <transactionPricePerShare>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <value>2021-08-04</value>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F3"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>145518</value>
                    <footnoteId id="F4"/>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">Cancellation of convertible debt without conversion.</footnote>
        <footnote id="F2">The convertible debt cancelled is comprised of $404,634 principal and $228,369 accrued interest as of March 6, 2023.</footnote>
        <footnote id="F3">The conversion right expires upon payment of the indebtedness in full.</footnote>
        <footnote id="F4">The principal and accrued interest were convertible at $4.35.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/Laura L. Barton, POA for James S. Pignatelli</signatureName>
        <signatureDate>2023-03-14</signatureDate>
    </ownerSignature>
</ownershipDocument>
