In this study, the thermal behavior of the phase change material (PCM) during melting process inside a shell-and-tube heat exchanger used in thermal energy storage (TES) systems has been investigated by numerical analysis with fin and without fin models. Two dimensional transient numerical analyzes have been carried out with the ANSYS Fluent commercial program using the computational fluid dynamics (HAD) approach. The study has been first validated for the without fin model with reference to an experimental study available in the literature. In this model, the effect of temperature of heat transfer fluid (HTF) on PCM melting time has evaluated by taking HTF's temperatures 50 degrees C, 60 degrees C and 70 degrees C. Then, 6, 9, 12 and 15 fins have been added to this model and the effect of the number of fins on the PCM melting time has been investigated. The results obtained in the numerical study show that as the HTF temperature and number of fins increase, the melting time of PCM decreases, so that PCM stores more rapidly the heat from HTF. It has been determined that the fin models with 6, 9, 12 and 15 which are 2,66, 3,49, 4,32 and 5,15 of fin effectiveness reduce the melting time by 72,5%, 76,7%, 78,4% and 80% respectively, according to without fin model.