The present work aims at studying the thermal and dielectric properties of addition-cure liquid silicone rubber (ALSR) matrix composites using boron nitride (BN) and aluminum nitride (AlN) as a hybrid thermal conductive filler. Composite samples with different filler contents were fabricated, and the density, thermal conductivity, thermal stability, dielectric properties, and volume resistivity of the samples were measured. According to the experimental results, the density, thermal conductivity, dielectric constant and dielectric loss tangent values all increased with the increasing addition of filler. When the weight fraction of hBN filler was 50 wt%, the thermal conductivity of composites was 0.554 W (m⁻¹ K⁻¹), which is 3.4 times higher than that of pure ALSR. The corresponding relative permittivity and dielectric loss were 3.98 and 0.0085 at 1 MHz, respectively. Furthermore, TGA results revealed that the AlN/BN hybrid filler could also improve the thermal stability of ALSR. The volume resistivity of ALSR composites was higher than that of pure ALSR. The addition of fillers improved the thermal properties of ALSR and had little effect on its insulation properties. This characteristic makes ALSR composites attractive in the field of insulating materials.