As a kind of essential hydrated salt phase change energy storage materials, mirabilite with high energy storage density and mild phase-transition temperature has excellent application potential in the problems of solar time and space mismatch. However, there are some disadvantages such as supercooling, substantial phase stratification and leakage problem, limiting its further applications. In this work, for the preparation of shaped mirabilite phase change materials (MPCMs), graphene (GO), sodium carboxymethyl cellulose (CMC), and carbon nanofibers (CNFs) were used as starting materials to prepare lightweight CMC/rGO/CNFs carbon aerogel (CGCA) as support with stable shape, high specific surface area, and well-arranged hierarchically porous structure. The results show that CGCA has regular layered plentiful pores and stable foam structure, and the pore and sheet interspersed structure in CGCA stabilizes PCMs via capillary force and surface tension. The hydrophilic aerogels supported MPCMs decrease mirabilite leaking and reduce supercooling to around 0.7‒1 °C. The latent heats of melting and crystallization of CGCA-supported mirabilite phase change materials (CGCA-PCMs) are 157.1 and 114.8 J·g−1, respectively. Furthermore, after 1500 solid‒liquid cycles, there is no leakage, and the retention rate of crystallization latent heat is 45.32%, exhibiting remarkable thermal cycling stability.