Aiming at the uncertaity of heat storage efficiency during the melting process of phase-change materials in the heat accumulator and the natural convection heat transfer process in the phase-change region, the influence of natural convection caused by gravity on the heat storage performance of the phase change heat storage was studied by numerical simulation with the tube-type solar phase change accumulator as the basic structure and the paraffin with 10% expanded graphite as the heat storage material. The results show that the natural convection caused by solid-liquid density difference has an obvious promoting effect on the phase change heat storage process. The heat storage time of the heat accumulator considering natural convection is nearly twice that of the heat accumulator without considering natural convection. The influence of natural convection on phase change materials in every region is different. In the early stage of melting of phase change materials, the melting rate above the innertube is faster due to the influence of natural convection of liquid phase. Based on the theoretical analysis and according to the characteristics of the melting rate and melting state of the heat accumulator, the melting process is segmented, which can further understand the heat storage process of the heat accumulator and provide certain theoretical guidance for optimizing the structure of the heat accumulator.