Energy storage technology provides a new direction for the utilization of renewable and sustainability energy. The objective of this study is to introduce a novel, wavy, longitudinal fin design, which aims to improve heat transfer in the melting process of a Latent Heat Thermal Energy Storage (LHTES) unit. The main goal is to mitigate the negative effects caused by the refractory zone at the end of the melting phase. A two-dimensional numerical model of LHTES unit is established by using the enthalpy porosity method and verified by experimental data. Through the quantitative comparison between the traditional rectangular fin and the innovative wave fin, the influence of wave fin on the heat transfer mechanism in the heat storage process is revealed. The results show that the average heat storage rate of five and six wave fins is 3.70% and 12.98% higher than that of conventional rectangular fins, respectively, and the average temperature response of six wave fins is 17.78% higher than that of conventional rectangular fins. The addition of the wave fin weakens the negative effect of the refractory zone, but prolongs the heating time of the initial melting point.