Hybrid graphene aerogels (HGA) consisting of graphene oxide (GO) and graphene nanoplatelets (GNP) were prepared and introduced into polyethylene glycol (PEG) via vacuum impregnation, aiming at obtaining composite phase change materials (PCMs) with high thermal conductivity, outstanding shape-stabilization, high energy storage density, commendable thermal repeatability and the ability to light-to-heat energy storage. GO nanosheets formed a three-dimensional supporting network to keep the shape of PEG stable during phase change and GNP dispersed uniformity along the network structure of GO and thus a thermal conductive pathway was constructed. The incorporation of HGA remarkably enhanced the thermal conductivity and shape-stabilization of the composite PCMs. The PEG/HGA composite PCM with only ca. 0.45 wt% GO and ca. 1.8 wt% GNP, showed an enhanced thermal conductivity of 1.43 W/mK from 0.31 W/mK of pure PEG and an improvement of 361%, much higher than the improvement that can be achieved by solution or melt blending. Moreover, an energy conversion from light to heat was realized with the composite PCMs. Thus, this work provides a simple, green and environmentally friendly way to achieve simultaneous enhancement of the thermal conductivity, energy storage density and shape-stabilization of PCMs and realize light-to-thermal energy conversion.