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

    <schemaVersion>X0206</schemaVersion>

    <documentType>3</documentType>

    <periodOfReport>2020-03-12</periodOfReport>

    <noSecuritiesOwned>0</noSecuritiesOwned>

    <issuer>
        <issuerCik>0001595248</issuerCik>
        <issuerName>Genprex, Inc.</issuerName>
        <issuerTradingSymbol>GNPX</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001177176</rptOwnerCik>
            <rptOwnerName>VACZY CATHERINE M</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>1601 TRINITY STREET</rptOwnerStreet1>
            <rptOwnerStreet2>BLDG B, SUITE 3.322</rptOwnerStreet2>
            <rptOwnerCity>AUSTIN</rptOwnerCity>
            <rptOwnerState>TX</rptOwnerState>
            <rptOwnerZipCode>78712</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isOfficer>1</isOfficer>
            <officerTitle>EVP &amp; Chief Strategy Officer</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <derivativeTable>
        <derivativeHolding>
            <securityTitle>
                <value>Stock Option (right to buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>2.0000</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <value>2020-03-12</value>
                <footnoteId id="F1"/>
            </exerciseDate>
            <expirationDate>
                <value>2030-03-11</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>540000</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">1/36 of the shares subject to the option shall vest on 3/12/20, and an additional one-thirty-sixth (1/36) of the shares subject to the option shall vest on each monthly anniversary of 03/12/20, provided that the optionee continues to serve as a Service Provider (as defined in Genprex, Inc. 2018 Equity Incentive Plan) through the applicable vesting date.</footnote>
    </footnotes>

    <ownerSignature>
        <signatureName>/s/ Catherine M. Vaczy</signatureName>
        <signatureDate>2020-03-12</signatureDate>
    </ownerSignature>
</ownershipDocument>
