We reported thermal properties of the epoxy‐based hybrid composites with graphene and Cu‐NP fillers. The high thermal conductivity of 13.5 ± 1.6 Wm−1K−1 was achieved for epoxy composites with the binary fillers of 40 wt% of graphene and 35 wt% of Cu‐NPs. It was found that the thermal conductivity of composites with a moderate graphene concentration of fg = 15 wt% exhibits an abrupt increase as the loading of Cu‐NPs approaches fCu ≈ 40 wt %, followed by saturation. In contrast, in composites with a high graphene concentration, fg = 40 wt%, the thermal conductivity increases linearly with addition of Cu‐NPs. It was also established that at low graphene concentrations of 5 wt%, addition of Cu‐NPs results in the thermal percolation prior to the electrical percolation. This finding has important implications for the design of TIMs. At all concentrations of the fillers, below and above the electrical percolation threshold, the thermal transport is dominated by phonons. The obtained results shed light on the interaction between graphene fillers and Cu‐NPs in the composites, and demonstrate potential of such hybrid epoxy composites for practical applications in TIMs and adhesives.