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

    <schemaVersion>X0203</schemaVersion>

    <documentType>3</documentType>

    <periodOfReport>2008-10-10</periodOfReport>

    <noSecuritiesOwned>0</noSecuritiesOwned>

    <issuer>
        <issuerCik>0001393718</issuerCik>
        <issuerName>SP Acquisition Holdings, Inc.</issuerName>
        <issuerTradingSymbol>DSP</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001132413</rptOwnerCik>
            <rptOwnerName>MILLENCO, L.L.C.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O MILLENNIUM MANAGEMENT LLC</rptOwnerStreet1>
            <rptOwnerStreet2>666 FIFTH AVENUE, 8TH FLOOR</rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10103-0899</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001273087</rptOwnerCik>
            <rptOwnerName>MILLENNIUM MANAGEMENT, L.L.C.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>666 FIFTH AVENUE, 8TH FLOOR</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10103-0899</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>1</isOther>
            <otherText>May be deemed a group member.</otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001017456</rptOwnerCik>
            <rptOwnerName>ENGLANDER ISRAEL A</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O MILLENNIUM MANAGEMENT, L.L.C.</rptOwnerStreet1>
            <rptOwnerStreet2>666 FIFTH AVENUE, 8TH FLOOR</rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10103-0899</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>1</isOther>
            <otherText>May be deemed a group member.</otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>6018550</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                    <footnoteId id="F3"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F4"/>
                    <footnoteId id="F5"/>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value></value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">As of the date of this filing, Millenco LLC, a Delaware limited liability company (&quot;Millenco&quot;), is the beneficial owner of 6,018,550 shares of common stock, par value $0.001 per share (&quot;Common Stock&quot;) of SP Acquisition Holdings, Inc. (the &quot;Issuer&quot;), of which 1,785,250 are a constituent part of the Issuer's units (&quot;Units&quot;), of which Millenco holds 1,785,250.  Each Unit consists of one share of Common Stock and one warrant to purchase the Issuer's Common Stock (&quot;Warrant&quot;).</footnote>
        <footnote id="F2">Each Warrant entitles the holder to purchase one share of the Issuer's Common Stock at a price of $7.50. The Warrants will become exercisable on the later of one year from the date of the final prospectus relating to the Issuer's initial public offering or the Issuer's completion of a business combination, provided in each case that the Issuer has an effective registration statement covering the shares of Common Stock issuable upon the exercise of the Warrants and a current prospectus relating to them is available.  The Warrants will expire five years from the date of the Issuer's prospectus, dated October 10, 2007, or earlier upon redemption. As of the date of this filing, the Issuer has not announced the completion of a business combination and therefore, the Warrants are not currently exercisable.</footnote>
        <footnote id="F3">In addition to the 1,785,250 Warrants held by Millenco as a constituent part of the Units, Millenco holds an additional 1,376,100 Warrants, which are also not currently exercisable.  Catapult Partners, Ltd., an affiliate of the Reporting Persons, holds 1,017,500 Warrants, which are also not currently exercisable.</footnote>
        <footnote id="F4">Millennium Management LLC, a Delaware limited liability company (&quot;Millennium Management&quot;), is the manager of Millenco, and consequently may be deemed to have shared voting control and investment discretion over securities owned by Millenco. Israel A. Englander (&quot;Mr. Englander&quot;) is the managing member of Millennium Management. As a result, Mr. Englander may be deemed to have shared voting control and investment discretion over securities deemed to be beneficially owned by Millennium Management. The foregoing should not be construed in and of itself as an admission by Millennium Management or Mr. Englander as to beneficial ownership of the shares owned by Millenco.</footnote>
        <footnote id="F5">The foregoing should not be construed in and of itself as an admission by Millennium Management or Mr. Englander as to beneficial ownership of the shares owned by Millenco.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>Mark Meskin, Chief Executive Officer</signatureName>
        <signatureDate>2008-10-14</signatureDate>
    </ownerSignature>
</ownershipDocument>
