-----BEGIN PRIVACY-ENHANCED MESSAGE-----
Proc-Type: 2001,MIC-CLEAR
Originator-Name: webmaster@www.sec.gov
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 TWSM7vrzLADbmYQaionwg5sDW3P6oaM5D3tdezXMm7z1T+B+twIDAQAB
MIC-Info: RSA-MD5,RSA,
 SzXmedYlYxKtSztqs4mrx+dY8aeurA2Se32t6YGKwd4DKY+QJWwMYpw1ejVgHPB9
 zH9LJH49Hhy3DHtSb/CRHw==

<SEC-DOCUMENT>0001140361-06-008047.txt : 20060524
<SEC-HEADER>0001140361-06-008047.hdr.sgml : 20060524
<ACCEPTANCE-DATETIME>20060524144629
ACCESSION NUMBER:		0001140361-06-008047
CONFORMED SUBMISSION TYPE:	4
PUBLIC DOCUMENT COUNT:		1
CONFORMED PERIOD OF REPORT:	20060523
FILED AS OF DATE:		20060524
DATE AS OF CHANGE:		20060524

REPORTING-OWNER:	

	OWNER DATA:	
		COMPANY CONFORMED NAME:			Cribbs Richard B
		CENTRAL INDEX KEY:			0001363556

	FILING VALUES:
		FORM TYPE:		4
		SEC ACT:		1934 Act
		SEC FILE NUMBER:	000-24960
		FILM NUMBER:		06863926

	BUSINESS ADDRESS:	
		BUSINESS PHONE:		423-821-1212

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

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>2006-05-23</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001363556</rptOwnerCik>
            <rptOwnerName>Cribbs Richard B</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>Controller</officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Employee Stock Option (Right-to-Buy) Class A common stock</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>12.79</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2006-05-23</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>2500</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F1"/>
            </exerciseDate>
            <expirationDate>
                <value>2016-05-23</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Class A common stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>2500</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>2500</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value></value>
                </natureOfOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">The option to purchase 2,500 shares of Class A common stock is exercisable between May 23, 2007 and May 23, 2009, at the rate of one-third per year.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Richard B. Cribbs, by Heidi Hornung-Scherr, attorney-in-fact, pursuant to a POA as previously filed with the SEC</signatureName>
        <signatureDate>2006-05-24</signatureDate>
    </ownerSignature>
</ownershipDocument>
</XML>
</TEXT>
</DOCUMENT>
</SEC-DOCUMENT>
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