The focus of the present study is the numerical simulation of multiple moving solid-liquid interfaces during natural-convection-dominated melting of a pure material contained in a vertical square enclosure imposed with time-periodic large-amplitude oscillatory wall temperature. A solution algorithm extended from the method developed in a previous study is used and demonstrated to be capable of tracking the multiple moving boundaries due to the time-periodic large-amplitude wall-temperature oscillation crossing the fusion point of the phase-change medium confined in the enclosure. The numerical results unveil interesting re-solidification and/or re-melting phenomena in accordance with the wall-temperature oscillation. There may coexist three solid-liquid interfaces during the sustained periodic solid-liquid phase-change process inside the enclosure. Accordingly, a complicated cyclic variation of the melting rate and the heat transfer characteristics arises as a result of the periodic occurrence of multiple moving boundaries inside the enclosure.