A novel form-stable phase change material (FSPCM) with remarkable improvement in thermal properties was fabricated by incorporating ternary fatty acid eutectics with graphene sheetconnected electrospun carbon nanofibers (GCNFs). The GCNFs possessed three-dimensional (3D) porous architecture and large specific surface area while provided mechanical support for FSPCM and effectively prevented flow/leakage of molten fatty acid. The GCNF based FSPCM exhibited desire structural morphology with lauric-myristic-stearic acid (LA-MA-SA) eutectic mixture being well dispersed in a 3D porous architecture. This novel FSPCM demonstrated superior thermal storage/retrieval capability and temperature regulation ability as well as good shape stability and thermal cycling stability. The melting and crystallization enthalpies of the fabricated FSPCMs were up to 120.4 and 120.1 kJ/kg, respectively. The thermal conductivity of the fabricated FSPCMs was 337% and 188% higher than that of LA-MA-SA eutectic mixture and a control sample without graphene, respectively, which ranked the top among the literature about LA-MA-SA eutectic mixture derived composite FSPCMs. Furthermore, the heating/cooling efficiency of the prepared FSPCMs was 45.7/64.9% higher than that of LA-MA-SA eutectic mixture.