Latent heat storage (LHS) on ships using phase change materials (PCMs) is challenged by inefficient heat storage efficiency and susceptibility to sloshing conditions. To address this issue, this paper proposes a shell-and-tube LHS unit using innovative fins. The enthalpy-porosity approach is employed to study the melting characteristics of LHS units under sloshing, focusing on the effects of direction, frequency, and strength of sloshing conditions. An optimal fin configuration to enhance thermal storage performance under sloshing is proposed. The results indicate that the sloshing conditions effectively enhance the temperature uniformity and heat storage capacity of LHS units. Compared with the slosh-free condition, the full melting duration of PCMs in LHS units under roll and heave conditions is reduced by 20.9 % and 23.6 %, respectively. Moreover, the natural convection intensity and heat transfer uniformity under sloshing conditions increase significantly, improving the heat transport capacity in the late melting stage. Additionally, the heat storage capacity of LHS units improves with a decrease in sloshing frequency and an increase in sloshing strength; however, there is a limit to the performance enhancement gains. Interestingly, the arrangement of fins closest to the refractory zone effectively improves the heat transport in the later melting stage, resulting in a further 6.8% increase in the melting rate.