Melting process inside in a vertical cylinder has been investigated numerically to observe heat transfer characteristics in the latent heat storage vessel applied to the thermal storage system. The time-dependent boundary fitted coordinate system was introduced to overcome the difficulty caused by the moving boundary. The present results are in good agreement with the available previous data when the initial subcooling effect of the solid phase is not considered. It is found that the melting is promoted by the natural convection, but is delayed by the initial subcooling effect of the solid phase.