In this work, a numerical study is proposed to investigate and predict the thermal performance of graphite foams infiltrated with phase change materials, PCMs, for space and terrestrial energy storage systems. The numerical model is based on a volume averaging technique while a finite volume method has been used to discretize the heat diffusion equation. A line-by-line solver based on tri-diagonal matrix algorithm has been used to iteratively solve the algebraic discretization equations. Because of the high thermal conductivity of graphite foams, the PCM-foam system thermal performance has been improved significantly. For space applications, the average value of the output power of the new energy storage system has been increased by more than eight times. While for terrestrial applications, the average output power using carbon foam of porosity 97% is about five times greater than that for using pure PCM.