In this paper, a novel design of multitube shell and tube latent heat thermal energy storage system (LHTES) with variable porosity metal matrix in PCM is presented. The shell side of the LHTES contains a phase change material, whereas heat transfer fluid (HTF) flows through seven tubes with internal fins. Metal matrix, as a thermal conductivity enhancer (TCE), is used to augment heat transfer in PCM, however the temperature distribution in PCM is found to be non-uniform along the length of the storage system for constant porosity metal matrix in PCM, which affects the thermal performance of the LHTES. A numerical model is developed to investigate the fluid flow and heat transfer characteristics using the momentum equation and the two-temperature non-equilibrium energy equation coupled with the enthalpy method to account for phase change in PCM. The numerical model is first validated with the experimental results and further extended to identify the effects of geometrical parameters on the temperature distribution in PCM. A relationship between porosity and ratio of length to annular diameter of the storage system is developed for porosity varying from 0.95 to 0.85. It is found that the size of LHTES with variable metal matrix porosity can be reduced for the same effectiveness.