Currently, epoxy-based composites are widely used in thermal management. However, with the development of complex and high power-density electronic devices, the thermal properties of the composites need to be improved. Inspired by the unique galls-leaf structure of Distylium chinense, a graphene-diamond framework (GRDF) is developed by a simple filtration method. A through-plane and in-plane thermal conductivity of 22.7 and 21.8 Wm⁻¹ K⁻¹, respectively, have been achieved by forming epoxy-based composites with the GRDF annealed at 3000 °C. The result is 70% higher than the best-reported value for epoxy-based composites prepared by vacuum filtration under a filler content of 43 wt%. Such high thermal conductivity remains unchanged (within 2%) in a temperature range from 25 to 100 °C. Based on various microscopic characterizations, the diamond particles evenly distribute in a framework formed by graphene sheets, which bridge the gaps in the framework and improve its structural integrity. High-temperature annealing converts most diamond particles to graphite, which further enhances the thermal properties of the composite. The observations provide a feasible way for developing polymer-based composite with high thermal conductivity, which could meet the ever-increasing demands for heat dissipation in high-power electronics.