In this work, we introduced highly thermally conductive and fibrous amino multi-walled carbon nanotubes (MCNT-NH2) into hexagonal boron nitride/liquid crystal epoxy resin (h-BN/LCER) composites to improve the thermal conductivity of the composites. First, we prepared hexagonal boron [email protected] multi-walled carbon nanotubes ([email protected]) hybrid fillers. Then, the amino group in the hybrid filler participated in the curing process of the epoxy resin to prepare hexagonal boron [email protected] multi-walled carbon nanotubes/liquid crystal epoxy resin ([email protected]/LCER) composites. Subsequently, its thermal conductivity was tested and analyzed using the Agari’s model and microstructure of the composites, and we can come to conclude that the thermal conductivity of [email protected]/LCER composites is higher than that of h-BN/LCER at the same filler content. The main reason is that the addition of MCNT-NH2 plays a role in increasing the thermal conduction path of h-BN/LCER composites and decreasing the large interface thermal resistance of fillers and resin matrix. Finally, the usability and thermal conductivity of [email protected]/LECR composites were verified by light-emitting diode (LED) lamps. The temperature of LED lamp using 50% [email protected]/LCER composites was eventually stabilized at 27.7 °C, it is expected that 50% [email protected]/LCER composites will be used in LED electronic products.