Ice thermal storage (ITS) performance for cooling systems is greatly influenced by the poor thermal conductivity of phase change material (PCM). The effect of natural convection on the melting process is significant for heat transfer enhancement. Thus, the melting performance of PCM in a shell-and-tube latent heat storage (STLHS) unit is numerically studied by considering natural convection in terms of various heat source positions and configurations, i.e., central position, eccentric position, and flat-tube type. Temperature distribution, melting time, and the overall heat transfer coefficient during the process are investigated. The results show that the circulation vortex formed by natural convection is a dominant factor that affects melting front evolution and the overall heat transfer coefficient. When input heat flux is relatively weak, PCM below the heat source is liquefied first. In contrast, PCM in the upper part melts earlier when the heat flux is excellent. The overall heat transfer coefficient decreases sharply with the increase in melting time in the early stage. Then, the heat transfer coefficient tends to be constant. PCM in an STLHS unit with a heat source in a lower position and a configuration of vertical flat-tube type has a desirable performance when compared with other cases, which could provide good support for ITS application.