The leakage of organic phase change materials (OPCMs) at temperatures above their melting point severely limits their large-scale application. The introduction of porous supports has been identified as an efficient leakageproofing method. In this study, a novel carbonized Cu-coated melamine foam (MF)/reduced graphene oxide (rGO) framework (MF/rGO/Cu-C) is constructed as a support for fabricating stabilized multifunctional OPCMs. MF serves as the supporting material, while rGO and Cu act as functional reinforcements. As a thermal energy storage material, polyethylene glycol (PEG) is encapsulated into MF/rGO/Cu-C through a vacuum-assisted impregnation method to obtain PEG@MF/rGO/Cu-C composite with excellent comprehensive performance. PEG@MF/rGO/Cu-C exhibits high phase change enthalpies of 148.3 J g −1 (melting) and 143.9 J g −1 (crystallization), corresponding to a high energy storage capability of 92.7%. Simultaneously, MF/rGO/Cu-C endues the composite with an enhanced thermal conductivity of 0.4621 W m −1 K −1 , which increases by 463% compared to that of PEG@MF. Furthermore, PEG@MF/rGO/Cu-C displays great light-to-thermal and electric-to-thermal conversion capabilities, thermal cycle stability, light-tothermal cycle stability, and shape stability, showing promising application prospects in different aspects.