Efficient thermal management materials have become one of the main challenges faced by the rapid development of current electronic technology. In this study, a covalent bond was first designed to connect carbon nanotubes (CNTs) and boron nitride (BN) to prepare CNTs@BN hybrids, and then the prepared CNTs@BN hybrids were used to enhance the thermal conductivity of ethylene-vinyl acetate (EVA) matrix. The results indicated that the covalent bond connections between CNTs and BN effectively reduced the interfacial thermal resistance and promoted the construction of a continuous and efficient heat conduction network. Finally, the thermal conductivity of EVA composite reached 7.84 W m −1 K −1 , which was 2613% higher than that of EVA matrix. The sensitive response of EVA composite to temperature further demonstrated its excellent thermal management capability. The EVA composite also had good thermal stability and stable electrical insulation performance, which further guaranteed its application in electronic equipment. • A covalent bond was designed to connect CNTs and BN to prepare CNTs@BN hybrids. • The agglomeration of CNTs was avoided and the interfacial interaction between BN and EVA was improved. • The covalent bond connections between CNTs and BN reduced the interfacial thermal resistance. • EVA/CNTs@BN composite had good thermal stability, mechanical strength and electrical insulation properties.