With the aim of an efficient thermal energy storage, this study was carried out on the phase change process in a double-pipe latent heat storage system incorporating sinusoidal wavy fins during both melting and solidification and the outcomes were compared with that for smooth and non-finned units. The phase change material is in the outer side while the water (heat transfer fluid) is passed through the inner side which formed a vertical double tube. The investigation on the performance of different wave-amplitudes and wavelengths of the wavy fins lead to the qualification of the best wave profile. The characteristics of the water flow were also examined. The numerical results reflect that, for the best wavy profile, with the wave-amplitude and wavelength of 2 and 1 mm, respectively, the time for melting and solidification reduces by 43.49% and 17.81%, compared with that of the non-finned unit while they are 7.7% and 4.45% compared to the smooth fin case. Furthermore, sensitivity analysis of the Reynolds number and inlet temperature of water indicates that higher Reynolds number and the temperature difference between the inlet water and melting point result in a time reduction in the charging and discharging.