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

    <schemaVersion>X0303</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2010-12-07</periodOfReport>

    <issuer>
        <issuerCik>0001141719</issuerCik>
        <issuerName>ALTERRA CAPITAL HOLDINGS Ltd</issuerName>
        <issuerTradingSymbol>ALTE</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001072504</rptOwnerCik>
            <rptOwnerName>HARTZBAND MERYL D</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O ALTERRA CAPITAL HOLDINGS LIMITED</rptOwnerStreet1>
            <rptOwnerStreet2>ALTERRA HOUSE, 2 FRONT STREET</rptOwnerStreet2>
            <rptOwnerCity>HAMILTON, BERMUDA</rptOwnerCity>
            <rptOwnerState>D0</rptOwnerState>
            <rptOwnerZipCode>HM 11</rptOwnerZipCode>
            <rptOwnerStateDescription>BERMUDA</rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Warrants (right to buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>19.64</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2010-12-07</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>28962.5</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                    <footnoteId id="F3"/>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                    <footnoteId id="F3"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F4"/>
            </exerciseDate>
            <expirationDate>
                <value>2015-12-15</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Shares</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>28962.5</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>4848518.6</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                    <footnoteId id="F3"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Trident III Professionals Fund, L.P. and Trident III, L.P.</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                    <footnoteId id="F3"/>
                </natureOfOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">Filing is made in respect of warrants to purchase common shares of Alterra Capital Holdings Limited (&quot;Alterra&quot;) held by Trident III Professionals Fund, L.P. and Trident III, L.P. Ms. Hartzband is a member and senior principal of Stone Point Capital LLC, a shareholder and a director of Stone Point GP Ltd., which is the general partner of Trident III Professionals Fund, L.P., and a member of the investment committee and owner of one of the five general partners of Trident Capital III, L.P., which is the general partner of Trident III, L.P. Ms. Hartzband disclaims beneficial ownership of the common shares of Alterra held of record or beneficially by Trident III Professionals Fund, L.P. and Trident III, L.P., except as to the extent of any pecuniary interest therein.</footnote>
        <footnote id="F2">Pursuant to the anti-dilution provisions of warrants to purchase common shares of Alterra held by Trident III Professionals Fund, L.P. and Trident III, L.P., following the declaration of a dividend by Alterra, (i) each of Trident III Professionals Fund, L.P. and Trident III, L.P. is entitled to elect to receive a payment in cash in respect of such dividend for each common share of Alterra purchased pursuant to the warrants (such payment to be made at the time of exercise of the warrants), or (ii) if Trident III Professionals Fund, L.P. and Trident III, L.P. make no election, each of Trident III Professionals Fund, L.P. and Trident III, L.P. will receive an adjustment to the exercise price of the warrants held by them (and a resulting change to the number of common shares of Alterra for which its warrants are exercisable) following the record date for such dividend.</footnote>
        <footnote id="F3">On December 7, 2010, the exercise price of the warrants held by Trident III Professionals Fund, L.P. and Trident III, L.P. adjusted (and a resulting adjustment was made to the number of common shares for which its warrants are exercisable) in respect of the $0.12 per share dividend declared by Alterra to holders of record of common shares of Alterra as of November 16, 2010. Pursuant to this adjustment, the exercise price of the warrants held by each of Trident III Professionals Fund, L.P. and Trident III, L.P. was reduced from $19.75 to $19.64 and (a) Trident III Professionals Fund, L.P. became entitled to exercise its warrants for an additional 685.84 common shares of Alterra and (b) Trident III, L.P. became entitled to exercise its warrants for an additional 28,276.66 common shares of Alterra.</footnote>
        <footnote id="F4">All warrants are immediately exercisable.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>Bernard Asirifi, Attorney-in-Fact</signatureName>
        <signatureDate>2010-12-08</signatureDate>
    </ownerSignature>
</ownershipDocument>
