Latent heat storage technology is widely used in solar power generation. Aiming to enhance the energy utilization rate to a greater extent, an innovative fan-shaped structure has been proposed to construct the metal fins of the shell-and-tube thermal storage device. The enthalpy method is used to simulate the heat storage process and focuses on the influence of inlet conditions on heat transfer. The influence of the fin structure on the melting properties of phase change material has been studied. The results show that increasing inlet temperature and inlet flow rate is a convenient and effective way to improve energy efficiency. As the inlet temperature is increased from 343 K to 358 K, the total heat storage and energy efficiency are improved by 13.4% and 10.2%, respectively, and the melting time is reduced by 36.2%. As the flow rate is increased from 3 L/min to 9 L/min, the complete melting time is reduced by 33.4%. Energy efficiency peaks at a flow rate of 5 L/min. Reasonable optimization of the fin structure can enhance the natural convection circulation during the melting process and further improve the energy efficiency. The research results can guide the design and structural optimization of the finned tube heat storage device.