To develop a design and operational method for a BOG (Boil-off-Gas) re-liquefaction process for the LNG cold energy storage system, we performed numerical simulation analysis on freezing and melting processes of n-pentane used as a PCM (Phase-Change Material) in the system. Based on the results of a pilot-plant test reported in our previous papers, we adopted a simplified thick-wall cylinder model in the calculation to describe the heat-transfer and phase-change phenomena around the finned tube and simplify the simulation procedure to operating commercial plants. Numerical calculations agreed well with the results obtained in the pilot-plant test and showed that the model can predict well the performance of the finned-tube latent heat storage unit with nearly the same length scale as the commercial equipment. Hence the model can be effectively used for designing a liquefaction process including a cold energy storage unit of this type and for supporting the plant operations. In addition, the analysis shows that the liquefaction time as well as the amount of discharged cold energy for the melting process decreases considerably when the length of the liquefaction zone in the finned tube exceeds the total length of the storage unit.