The invention belongs to the technical field of a heat conduction polymer composite material, and particularly relates to an epoxy composite material with high heat conductivity and a preparation method thereof. Firstly, electronegative graphene oxide nanosheets or boron nitride nanosheets are repeatedly deposited on the surface of commercial melamine sponge through layer-by-layer self assembly; a composite sponge framework with a three-dimensional filling network is formed; then, the composite sponge is subjected to epoxy resin encapsulation; the final heat conduction composite material is obtained. The materials can build and form a three-dimensional heat conduction network under the condition of extremely low filling adding quantity; when the boron nitride content is 1.7 weight percent and the graphene content is 0.74 weight percent, the heat conductivity in the vertical surface of the materials respectively reaches 0.62 W/Mk and 0.73 W/Mk. The method has the advantages that the operation is simple; the production cost is very low; the batch and scale production is easily realized; wide application prospects are realized.