In this study, silver–polydopamine–hexagonal boron nitride (h-BN@Ag) particles were prepared using mussel chemistry and reducibility of catechol. The modified method was simple and eco-friendly. In addition, we prepared h-BN@Ag/polyimide (PI) composite films via in situ polymerization, the scraper method, and thermal imidization. Owing to the good dispersion of the h-BN@Ag filler particles in the PI matrix and the bridging role of the Ag nanoparticles, the thermal conductivities of the h-BN@Ag/PI composite films were higher than that of the pure PI film. The thermal conductivity of the h-BN@Ag/PI film with the filler content of 10 wt% was 0.382 W (m·K)−1, which was 108% higher than that of pure PI films (0.184 W (m·K) −1). Furthermore, the composite films presented extremely low dielectric permittivity and loss tangent. Moreover, the heat resistance index of the composite films (304.6°C) was higher than that of pure PI (294.3°C). Thus, h-BN@Ag/PI composite films could be promising electronic packaging materials.