With rapid advances in electronic device miniaturization and increasing power density, high thermal conductivity polymer composites with excellent properties are becoming increasingly significant for the progress of next-generation electronic apparatuses. In this work, a new type of three-dimensional (3D) network silicon carbide (SiC) frame and core-shell SiC@SiO2 (SiC@SiO2) were successfully prepared. The effects of different filler forms (dispersed particle filler and three-dimensional continuous filler network) on the thermal conductivity of the composites were compared. The composites based on the three-dimensional filler network exhibited evidently better thermal conductivity improvement rates, compared to their traditional counterparts. The thermal conductivity of the epoxy/SiC@SiO2 composite having a total filler content of 17.0 vol% was 0.857 W/m/K, 328.5% higher than that of pure epoxy resin. Similarly, the thermal conductivity of the EP/3D-SiC composite having a total filler content of 13.8 vol% was 1.032 W/m/K, 416.0% higher than that of pure epoxy resin. The abovementioned stats were proven via molecular simulations. We estimated the interfacial thermal resistance (ITR) of the EP/3D-SiC composite to be 5.98 × 10−8 m2 K/W, which was an order of magnitude lower than that of the epoxy composites without a 3D network. Simultaneously, computerized molecular simulation technology was used to verify the feasibility of the experiment, which provided new ideas for the preparation of other highly thermally conductive materials.