Recently, graphene foam (GF) with a three-dimensional (3D) interconnected network produced by template-directed chemical vapor deposition (CVD) has been used to prepare composite phase-change materials (PCMs) with enhanced thermal conductivity. However, the pore size of GF is as large as hundreds of micrometers, resulting in a remarkable thermal resistance for heat transfer from the PCM inside the large pores to the GF strut walls. In this study, a novel 3D hierarchical GF (HGF) is obtained by filling the pores of GF with hollow graphene networks. The HGF is then used to prepare a paraffin wax (PW)-based composite PCM. The thermal conductivity of the PW/HGF composite PCM is 87% and 744% higher than that of the PW/GF composite PCM and pure PW, respectively. The PW/HGF composite PCM also exhibits better shape stability than the PW/GF composite PCM, negligible change in the phase-change temperature, a high thermal energy storage density that is 95% of pure PW, good thermal reliability, and chemical stability with cycling for 100 times. More importantly, PW/HGF composite PCM allows light-driven thermal energy storage with a high light-to-thermal energy conversion and storage efficiency, indicating its great potential for applications in solar-energy utilization and storage.