The thermally conductive properties of silicone thermal grease enhanced by hexagonal boron nitride (hBN) nanosheets as a filler are relevant to the field of lightweight polymer-based thermal interface materials. However, the enhancements are restricted by the amount of hBN nanosheets added, owing to a dramatic increase in the viscosity of silicone thermal grease. To this end, a rational structural design of the filler is needed to ensure the viable development of the composite material. Using reduced graphene oxide (RGO) as substrate, three-dimensional (3D) heterostructured reduced graphene oxide-hexagonal boron nitride (RGO-hBN)-stacking material was constructed by self-assembly of hBN nanosheets on the surface of RGO with the assistance of binder for silicone thermal grease. Compared with hBN nanosheets, 3D RGO-hBN more effectively improves the thermally conductive properties of silicone thermal grease, which is attributed to the introduction of graphene and its phonon-matching structural characteristics. RGO-hBN/silicone thermal grease with lower viscosity exhibits higher thermal conductivity, lower thermal resistance and better thermal management capability than those of hBN/silicone thermal grease at the same filler content. It is feasible to develop polymer-based thermal interface materials with good thermal transport performance for heat removal of modern electronics utilising graphene-supported hBN as the filler at low loading levels.