Epoxy (EP) is the preferred packaging materials used as a crucial component in power semiconductor devices. However, its low thermal conductivity (TC) always has negative impact in the heat dissipation of electronic devices. In this paper, we use hole-making method to prepare three-dimensional boron nitride ceramics-carbon (3D-BN-C) hybrids which are filled in EP matrix to improve the TC of the 3D-BN-C/EP composites. The results show that TC values of 3D-BN-C/EP composites are much superior to the BN/EP composite with random distribution of BN and 3D-BN/EP composite without carbon. The improved TC is mainly attributed to the high TC-3D skeleton structure and the low interface thermal resistance (R) due to the carbon connected with BN fillers. Infrared thermal images and Comsol simulation demonstrate that high TC 3D-BN-C/EP composite offers excellent heat dissipation capability of EP composites used as packing insulation materials. In addition, the dielectric loss of 3D-BN-C/EP composite still remains at a relative low level in a wide frequency range, exhibiting good insulation property and great potential to be used as high-performance packing insulation materials in electronic device applications.