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<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>0001298786</rptOwnerCik>
            <rptOwnerName>Gold Alan D</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>1</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>Chairman, President and CEO</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

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                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2016-01-27</value>
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            <deemedExecutionDate></deemedExecutionDate>
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                <footnoteId id="F1"/>
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            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>555433</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>23.8239</value>
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                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
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                <directOrIndirectOwnership>
                    <value>D</value>
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            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
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                    <value>17144</value>
                </transactionShares>
                <transactionPricePerShare>
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                <transactionAcquiredDisposedCode>
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                <value>2005-10-01</value>
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                <underlyingSecurityTitle>
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            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By SciMed Prop III, Inc.</value>
                </natureOfOwnership>
            </ownershipNature>
        </derivativeTransaction>
        <derivativeTransaction>
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                <value>Limited Partnership Units</value>
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            <transactionTimeliness>
                <value></value>
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                    <footnoteId id="F4"/>
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            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By SunMar Investments, Inc.</value>
                </natureOfOwnership>
            </ownershipNature>
        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
                <value>Limited Partnership Units</value>
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                <value>2016-01-27</value>
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            <transactionTimeliness>
                <value></value>
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            <transactionAmounts>
                <transactionShares>
                    <value>928098</value>
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            <expirationDate>
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                <sharesOwnedFollowingTransaction>
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                </sharesOwnedFollowingTransaction>
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            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
                <value>LTIP Units</value>
                <footnoteId id="F5"/>
            </securityTitle>
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                <footnoteId id="F5"/>
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            <transactionDate>
                <value>2016-01-27</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
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                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F8"/>
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            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
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                <transactionShares>
                    <value>52500</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>23.8239</value>
                    <footnoteId id="F8"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
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            <exerciseDate>
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            <expirationDate>
                <footnoteId id="F7"/>
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            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
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                <underlyingSecurityShares>
                    <value>52500</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
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                    <value>0</value>
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            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
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        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
                <value>LTIP Units</value>
                <footnoteId id="F5"/>
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            <conversionOrExercisePrice>
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            <transactionDate>
                <value>2016-01-27</value>
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            <transactionTimeliness>
                <value></value>
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            <transactionAmounts>
                <transactionShares>
                    <value>12950</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F4"/>
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                <transactionAcquiredDisposedCode>
                    <value>D</value>
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            <expirationDate>
                <footnoteId id="F7"/>
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            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>12950</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
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            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
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        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
                <value>Limited Partnership Units</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F2"/>
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            <transactionDate>
                <value>2016-01-27</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
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                <transactionFormType>4</transactionFormType>
                <transactionCode>D</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F4"/>
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            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>56822</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F4"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
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            <exerciseDate>
                <value>2005-10-01</value>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F3"/>
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            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>56822</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
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                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
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            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Children's Trust No.1</value>
                    <footnoteId id="F9"/>
                </natureOfOwnership>
            </ownershipNature>
        </derivativeTransaction>
        <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"/>
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            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>56822</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F4"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
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            <exerciseDate>
                <value>2005-10-01</value>
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            <expirationDate>
                <footnoteId id="F3"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>56822</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
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                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
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            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Children's Trust No.2</value>
                    <footnoteId id="F9"/>
                </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. 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.</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 and certain of the Reporting Person's LTIP 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>
        <footnote id="F5">Profits interest units of the Operating Partnership. The LTIP Units are subject to time-based restrictions.</footnote>
        <footnote id="F6">Upon the occurrence of certain &quot;triggering events,&quot; the LTIP Units can over time achieve full parity with common units of the Operating Partnership for all purposes. If such parity is reached, vested LTIP Units convert to common units of the Operating Partnership.</footnote>
        <footnote id="F7">The LTIP Units do not have an expiration date.</footnote>
        <footnote id="F8">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 received $23.8239 in cash in exchange for certain LTIP Units held by the Reporting Person.</footnote>
        <footnote id="F9">An irrevocable trust of which a family member of the reporting person is a trustee and of which one of the reporting person's adult children is the sole beneficiary.</footnote>
    </footnotes>

    <remarks></remarks>

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