In this work, the epoxy-based composites filled with 3-Aminopropyltriethoxysilane (KH-550) modified binary filler of hexagonal boron nitride (h-BN) flakes and h-BN whiskers were fabricated, and the thermal and dielectric properties of composites were systematically investigated. Adding h-BN whiskers to the filler could effectively form heat conduction paths and improve the phonon transmission efficiency, thereby improving the thermal conductivity of the composites. According to our results, the thermal conductivity of composite with 27 wt% h-BN flakes and 3 wt% h-BN whiskers reached up to 0.819 W·m−1·K−1, which was 3.9 times that of pure epoxy resin. At the same time, the dielectric loss value and dielectric constant of this composite at 1 MHz were 0.02678 and 4.55, respectively, while pure epoxy resin were 0.03602 and 4.33. In addition, introducing h-BN whiskers into the matrix could effectively improve the thermal stability and heat dissipation performance of composites.