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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2019-05-21</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001708405</issuerCik>
        <issuerName>Tremont Mortgage Trust</issuerName>
        <issuerTradingSymbol>TRMT</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001716421</rptOwnerCik>
            <rptOwnerName>Tremont Realty Advisors LLC</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>TWO NEWTON PLACE</rptOwnerStreet1>
            <rptOwnerStreet2>255 WASHINGTON STREET, SUITE 300</rptOwnerStreet2>
            <rptOwnerCity>NEWTON</rptOwnerCity>
            <rptOwnerState>MA</rptOwnerState>
            <rptOwnerZipCode>02458</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001613503</rptOwnerCik>
            <rptOwnerName>RMR Group LLC</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>TWO NEWTON PLACE</rptOwnerStreet1>
            <rptOwnerStreet2>255 WASHINGTON STREET, SUITE 300</rptOwnerStreet2>
            <rptOwnerCity>NEWTON</rptOwnerCity>
            <rptOwnerState>MA</rptOwnerState>
            <rptOwnerZipCode>02458</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001644378</rptOwnerCik>
            <rptOwnerName>RMR GROUP INC.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>TWO NEWTON PLACE</rptOwnerStreet1>
            <rptOwnerStreet2>255 WASHINGTON STREET, SUITE 300</rptOwnerStreet2>
            <rptOwnerCity>NEWTON</rptOwnerCity>
            <rptOwnerState>MA</rptOwnerState>
            <rptOwnerZipCode>02458</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Shares of Beneficial Interest</value>
            </securityTitle>
            <transactionDate>
                <value>2019-05-21</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>1000000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>5.65</value>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1600100</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                    <footnoteId id="F2"/>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Shares were acquired directly by Tremont Realty Advisors LLC (&quot;TRA&quot;) in a public offering transaction at $5.65 per share.</footnote>
        <footnote id="F2">All shares reported are held directly by TRA. TRA is a direct wholly owned subsidiary of The RMR Group LLC (&quot;RMR LLC&quot;), which is the direct majority owned operating subsidiary of The RMR Group Inc. (&quot;RMR Inc.&quot;). RMR Inc. and RMR LLC may be deemed to beneficially own the shares owned directly by TRA.</footnote>
    </footnotes>

    <ownerSignature>
        <signatureName>/s/ David M. Blackman, President, on behalf of Tremont Realty Advisors LLC</signatureName>
        <signatureDate>2019-05-22</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ Adam D. Portnoy, President, on behalf of The RMR Group LLC</signatureName>
        <signatureDate>2019-05-22</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ Adam D. Portnoy, President, on behalf of The RMR Group Inc.</signatureName>
        <signatureDate>2019-05-22</signatureDate>
    </ownerSignature>
</ownershipDocument>
