This study conducts numerical investigations on melting process in a shell-and-tube latent heat thermal energy storage (LHTES) unit with annular fins. Commercial grade paraffin is employed as the phase change material (PCM) and water serves as the heat transfer fluid (HTF). Finite-volume-method (FVM) based numerical simulations are performed to investigate the effects of fin number, height and thickness on the phase change process. Particular attention is made to justify the contribution of local natural convection to the overall phase change process. Results demonstrate that the full melting time could be maximally reduced by 65% by inserting annular fins into PCM. For maximizing thermal performance, an optimal group fin parameter (fin number N = 31, thickness t/l = 0.0248 and interval l/L = 0.0313) is recommended for the present study.