A systematic, carbon-based composite phase change materials with substantial increase of the thermal conductivity and energy storage density was assembled by encapsulating PEG into graphene foams (GF), CNTs and hierarchical porous materials derived from GF and CNT. The influence of preparation approaches on the microstructures, thermal conductivity and thermal energy densities of composites were assessed by various characterization tools. The results obtained indicated that graphene foam-CNT hybrid structures (GCNT) composites exhibit excellent thermal conductivity, 118% higher than pure PEG and 89.5% higher relative to that of GF/PEG@CNT (GPC) composites. The content and interconnected hierarchical porous carbons enhance thermal transfer in composites during the process of phase change. Notably, GCNT@PEG (GCP) had a maximum of up to 80 wt% PCM loading. This composite has a melting latent heat of 128.7 kJ/kg, up to 39.3% and 87.5% higher than those of other composites. CNTs have significantly enhanced the thermal transport of composite PCMs, but the interfacial thermal resistance of CNTs and graphene foam is the bottleneck of heat transfer of composite PCMs. The current results create the conditions for the application of novel hierarchical porous carbon composite PCMs for high-energy density, thermal energy conversion, and shape-stabilized PCMs (ssPCMs) with improved thermal conductivity.