Electronic power devices are moving towards high frequency, high integration, and high power, which urgently needs to develop high thermal conductive encapsulating insulation materials to improve the heat dissipation of electronic devices. Herein, we propose to modify the commercialized encapsulating materials of epoxy resin (EP) by incorporating three-dimensional hydroxylated boron nitride nanosheets (3D-BNNSs). The cryogel and vacuum freeze-drying techniques are employed to prepare the 3D-BNNSs using agarose. The results show that the constructed high thermal conductive structure of 3D-BNNSs can effectively enhance the thermal conductivity of EP and reduce the interfacial thermal resistance between BNNSs fillers. The thermal conductivity of 3D-BNNSs/EP composites with 33.03 wt% BNNSs reach 2.54 W/(m·K), which is 13.11 times higher than that of EP (0.18 W/(m·K)). Meanwhile, the resultant composites remain outstanding electrical insulation and dielectric properties. Because agarose contains numerous hydroxyl groups that can form hydrogen bonds with the hydroxyl groups on the surface-functionalized BNNSs, hydrogen bonding can lead to strong intermolecular interactions, which is conductive to accelarate phonon transport. Additionally, agarose can cross-link with the molecular chains of epoxy, impeding the movement of molecular chain segments and resulting in composites with low dielectric loss at high frequencies. This study demonstrates that the 3D-BNNSs/EP composites have great potential for application in thermal management of electronic components.