Phase change materials (PCMs) have wide applications in many fields and they are thought to be one of the highest potential materials in the future. Developing advanced PCMs faces various problems, such as low thermal conductivity, poor shape stability and single energy conversion pattern, etc. In this work, novel composite PCMs were fabricated based on the commercial melamine foam (MF) incorporated by the graphene oxide (GO) and graphene nanoplatelets (GNPs). After hydrothermal reaction and carbonization, the composite aerogel still maintained the three-dimensional (3D) composite framework structure with reduced GO (rGO) and GNPs covering on the carbonized MF framework. The composite PCM samples exhibited high shape stability without leakage under the load of 265 times of its own mass at temperature much higher than the phase change temperature of paraffin wax (PW), high phase change enthalpy retention rate (nearly 100% of PW), high thermal conductivity (1.46 W/m.K) and electrical conductivity (2.787 S/cm) at a filler content of 4.89 wt%. Moreover, the composite PCM samples have excellent light-to-thermal and electric-to-thermal energy conversion abilities, which endow the composite PCMs with great potential in diverse applications, such as the energy saving and heat preservation of building and temperature protection of microelectronic devices, etc.