The heat transfer enhancement performance of a phase change buried tubes thermal storage system is influenced by major parameters such as arrangement of heat transfer tubes, fin structure and fin geometry size. We developed a three-dimensional numerical model with two different arrangements and five different enhanced heat transfer structures respectively. For the sake of analysis the effects of arrangement of heat transfer tubes, fin structure and fin geometry size. In addition, we applied the enthalpy-transforming model to obtain the liquid fraction and location of the solid-liquid interface at different time in the phase change process. The numerical results show that the melting time of the thermal storage system model with a triangle arrangement is about 6.1% longer than that of the model with a square arrangement. Besides, the melting time of the model with 55 mm tube pitch is about 16.7% shorter than that of tube pitch with 60 mm. Moreover, the buried tube thermal storage system models with circle fins have the shortest melting time, which is 18 seconds. Melting time of the model with circle fins is about 40% shorter than that of the model with smooth tube. In addition, the melting time of the model with 3 mm fin thickness is 10 seconds, which is the shortest. The model with thicker fins means the shorter time of melting process. Moreover, the melting time of the model with 10.5 mm fin spacing is about 23.5% shorter than that of the model with 12.5 mm fin spacing, which is 13 seconds. In conclusion, the main factor of the melting time is the heat transfer area. It provides a guidance for the design and reconstruction of the type of heat storage structure.