The development of form-stable phase change materials (FSPCMs) with large latent heat, excellent thermal stability, and recyclability is essential for their practical applications for thermal or solar energy saving. Here, we first report the exploitation of fatty amines (FAs), in this case tetradecylamine (TDA) and octadecylamine (ODA), as novel organic phase change materials (PCMs) for fabrication of FSPCM composites with exceptional high energy density using porous 3D graphene sponge (GS) as porous supporting materials. The resulting fatty amines/graphene sponge composites (FAs/GS) show high latent heat of ranging from 293 kJ kg−1 to 303 kJ kg−1 and low supercooling degree of 7–9 °C. Surprisingly, it is found that the loading rate of these two FAs into GS is as high as 7063–10660 wt%, which is nearly three orders of magnitudes higher than that of most reported FSPCMs. In addition, compared with the FAs, the presence of GS results in an enhancement of thermal conductivity of FAs/GS. After 200 cycles of thermal cycling, the latent heat content of FAs/GS still remains as high as 93.34% (TDA/GS) and 93.83% (ODA/GS), implying an excellent thermal stability. Taking advantages of the merits mentioned above, the findings of this work would not only open a new way for exploiting the FAs as new high-performance organic PCMs, but also provide a possibility for construction of such FAs/GS with great potentials for real energy-saving applications based on their exceptional high energy density, low supercooling degree, unprecedented high loading value, excellent thermal stability and recycling capacity.