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Proc-Type: 2001,MIC-CLEAR
Originator-Name: webmaster@www.sec.gov
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 TWSM7vrzLADbmYQaionwg5sDW3P6oaM5D3tdezXMm7z1T+B+twIDAQAB
MIC-Info: RSA-MD5,RSA,
 NWTukf7/W+87ZPnA2TdGRrMaVSOBgIGNLordm42dCPSziZZUTKm67p2oO9Odou8L
 wg01QajulJdCowYmF+jnuA==

<SEC-DOCUMENT>0001140361-05-003386.txt : 20050503
<SEC-HEADER>0001140361-05-003386.hdr.sgml : 20050503
<ACCEPTANCE-DATETIME>20050503172136
ACCESSION NUMBER:		0001140361-05-003386
CONFORMED SUBMISSION TYPE:	4
PUBLIC DOCUMENT COUNT:		1
CONFORMED PERIOD OF REPORT:	20050429
FILED AS OF DATE:		20050503
DATE AS OF CHANGE:		20050503

REPORTING-OWNER:	

	OWNER DATA:	
		COMPANY CONFORMED NAME:			Miller Michael W
		CENTRAL INDEX KEY:			0001181040

	FILING VALUES:
		FORM TYPE:		4
		SEC ACT:		1934 Act
		SEC FILE NUMBER:	000-24960
		FILM NUMBER:		05796119

	BUSINESS ADDRESS:	
		BUSINESS PHONE:		8005320341

	MAIL ADDRESS:	
		STREET 1:		400 BIRMINGHAM HIGHWAY
		CITY:			CHATTANOOGA
		STATE:			TN
		ZIP:			37419

	FORMER NAME:	
		FORMER CONFORMED NAME:	MILLER MICHAEL W
		DATE OF NAME CHANGE:	20020819

ISSUER:		

	COMPANY DATA:	
		COMPANY CONFORMED NAME:			COVENANT TRANSPORT INC
		CENTRAL INDEX KEY:			0000928658
		STANDARD INDUSTRIAL CLASSIFICATION:	TRUCKING (NO LOCAL) [4213]
		IRS NUMBER:				880320154
		STATE OF INCORPORATION:			NV
		FISCAL YEAR END:			1231

	BUSINESS ADDRESS:	
		STREET 1:		400 BIRMINGHAM HIGHWAY
		CITY:			CHATTANOOGA
		STATE:			TN
		ZIP:			37419
		BUSINESS PHONE:		4238211212

	MAIL ADDRESS:	
		STREET 1:		400 BIRMINGHAM HIGHWAY
		CITY:			CHATTANOOGA
		STATE:			TN
		ZIP:			37419
</SEC-HEADER>
<DOCUMENT>
<TYPE>4
<SEQUENCE>1
<FILENAME>doc1.xml
<DESCRIPTION>FORM 4
<TEXT>
<XML>
<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0202</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2005-04-29</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000928658</issuerCik>
        <issuerName>COVENANT TRANSPORT INC</issuerName>
        <issuerTradingSymbol>CVTI</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001181040</rptOwnerCik>
            <rptOwnerName>Miller Michael W</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>400 BIRMINGHAM HIGHWAY</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>CHATTANOOGA</rptOwnerCity>
            <rptOwnerState>TN</rptOwnerState>
            <rptOwnerZipCode>37419</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>Exec Vice President &amp; COO</officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Class A Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2005-04-29</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>I</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>11490</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>13.42</value>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>11490</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>401(k)</value>
                    <footnoteId id="F2"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Price represents closing price on April 29, 2005. Because the 401(k) plan is unitized, it may not represent the actual transaction price.</footnote>
        <footnote id="F2">The number of shares reported beneficially owned following the reported transaction is equal to the reporting person's April 29, 2005, account balance in the employer stock fund under the issuer's 401(k) Plan divided by the closing price on April 29, 2005. The plan is unitized and as such does not itself allocate a specific number of shares to each participant.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Michael W. Miller, by Heidi Hornung-Scherr, attorney-in-fact, pursuant to a POA previously filed with the SEC</signatureName>
        <signatureDate>2005-05-03</signatureDate>
    </ownerSignature>
</ownershipDocument>
</XML>
</TEXT>
</DOCUMENT>
</SEC-DOCUMENT>
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