Polymer composites as thermal interface materials have been widely used in modern electronic equipment. In this work, we report a novel method to prepare highly through-plane thermally conductive silicone rubber (SR) composites with vertically aligned silicon carbide fibers (VA-SiCFs) entangled by SiC nanowires (SiCNWs) networks. First, a series of carbon fibers (CFs) skeletons were fabricated in sequence of coating poor thermally conductive polyacrylonitrile-based CFs with polydopamine, ice-templated assembly, and freeze-drying processes. Furthermore, VA-SiCFs networks, i.e., long-range continuous SiCFs-SiCNWs networks, based on the prepared CFs skeletons, were in-situ obtained via template-assisted chemical vapor deposition method. The thermal conductivity enhancement mechanism of VA-SiCFs networks on its SR composites was also intensively studied by finite element simulation, based on the first principles investigation of SiC, and Foygel’s theory. The in-situ grown VA-SiCFs networks possess high intrinsic thermal conductivity without the thermal interface between fillers, acting as the high-efficiency through-plane long-range continuous thermal conduction path, in which the SiCNWs were the in-plane “thermal spreader”. The VA-SiCFs/SR composites reached a high through-plane thermal conductivity, 2.13 W/(m·K), at the filler loading of 15 vol.%, which is 868.2%, and 249.2% higher than that of pure SR sample, and random-CFs@polydopamine (PDA)/SR composites at the same content, respectively. The VA-SiCFs/SR composites also exhibited good electrical insulation performance and excellent dimensional stability, which guaranteed the stable interfacial heat transfer of high-power density electronic devices.