Thermal interface materials (TIM) are key thermal management components to enhance the performance of electronic products, and how to improve thermal conductivity is a key issue to consider. As a high thermal conductivity material, it is difficult for copper to have both high thermal conductivity and high elasticity when filled into the polymer. In this paper, by growing copper nanoparticles on the surface of carbon felt (Cfelt), a three-dimensional interoperable thermally conductive copper network is formed with carbon fibers as the support, which makes the material both better thermally conductive and elastic at the same time. The vertical thermal conductivity of the prepared Cu-Cfelt/silicon rubber composite material reached 7.3230 W/mK. It is 23 times higher than pure silicon rubber(0.3130 W/mK), 18 times higher than Cu/silicon rubber composite (0.4120 W/mK) and 12 times higher than CFelt/silicon rubber composite (0.6200 W/mK), and successfully improves the thermal conductivity of the interface. The three-dimensional Cu network structure of the prepared Cu-CFelt/silicon rubber composite maximized the thermal conductivity of Cu, and the composite also showed excellent mechanical properties, indicating that the composite has broad application prospects in thermal management and other aspects.