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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2016-01-27</periodOfReport>

    <notSubjectToSection16>1</notSubjectToSection16>

    <issuer>
        <issuerCik>0001289236</issuerCik>
        <issuerName>BioMed Realty Trust Inc</issuerName>
        <issuerTradingSymbol>BMR</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001639638</rptOwnerCik>
            <rptOwnerName>Berens James R</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>17190 BERNARDO CENTER DRIVE</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>SAN DIEGO</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>92128</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>President, Wexford</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2016-01-27</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>D</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>18477</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>23.8239</value>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Limited Partnership Units</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F2"/>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2016-01-27</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>D</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F4"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>272491</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F4"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F2"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F3"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>272491</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Waterford Equities, LLC</value>
                </natureOfOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">In connection with the merger of BioMed Realty Trust, Inc. (the &quot;Company&quot;) with and into BRE Edison L.P., an affiliate of The Blackstone Group L.P. (the &quot;Merger&quot;) and the Agreement and Plan of Merger, dated as of October 7, 2015, among the Company, BioMed Realty, L.P. (the &quot;Operating Partnership&quot;) and affiliates of The Blackstone Group L.P., each holder of shares of common stock of the Company received $23.8239 in cash in exchange for each such share.</footnote>
        <footnote id="F2">Limited Partnership Units in the Operating Partnership. Limited Partnership Units are redeemable for cash based upon the fair market value of an equivalent number of shares of common stock of the Company, or, at the election of the Company, shares of the Company's common stock on a 1-for-1 basis.  Upon completion of the Merger, all of the Reporting Person's Limited Partnership Units became fully vested.</footnote>
        <footnote id="F3">The Limited Partnership Units have no expiration date.</footnote>
        <footnote id="F4">In connection with the merger of BRE Edison Acquisition L.P., an affiliate of The Blackstone Group L.P., with and into the Operating Partnership, and the Agreement and Plan of Merger, dated as of October 7, 2015, among the Company, the Operating Partnership and affiliates of The Blackstone Group L.P., the Reporting Person's Limited Partnership Units were converted into 5.5% Series B Cumulative Preferred Units of the surviving partnership in the merger on a one-for-one basis.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Jonathan P. Klassen, Attorney-in-fact</signatureName>
        <signatureDate>2016-01-29</signatureDate>
    </ownerSignature>
</ownershipDocument>
