The present study explored numerically the process of solidification of spherical phase change capsule, which spherical high-density polyethylene (HDPE)/paraffin shape stabilized phase change material (PCM) encapsulated by Calcium alginate. The mathematical model was solved numerically by using apparent heat capacity method. In simulation, it described the pore microstructure by the fractal geometry after the paraffin in capsule was extracted, and the volume change of paraffin in phase transformation and the cavity caused by manufacturing technology were also considered. Based on the fractal characterization, as one of the important physical properties of the HDPE/paraffin, the effective thermal conductivity was determined. The results show that The initial solidification process is almost unaffected when the volume change of the PCM is considered. However the heat transfer rate begins to shift to a significantly slower with the increment of solid rate. The initial cavity ratio influences the rate of the phase change heat transfer and reduces the phase change latent heat of each unit volume of capsule. The larger the size of spherical capsule, the greater the impact of Ste number on the complete solidification time. The conclusion would have important guidance significance to how to improve heat storage capacity and heat storage rate of the PCM.