Because of the latent heat of phase change, phase change materials (PCM) are used in thermal management in various fields. As a new energy source, lithium power batteries have been widely used in electric vehicles in recent years. As an effective passive cooling method, phase change cooling can effectively slow down the heat accumulation of lithium batteries. To apply phase change materials to alleviate the thermal runaway of lithium batteries, a paraffin/silver nanoparticle composite phase change material (CPCM) cylindrical system was established, and the phase change model and the volume of fluid (VOF) model were used to study the melting process of phase change materials. The change of the air/paraffin gas-liquid interface and the liquid phase distribution of the paraffin was obtained during the initial period, which was in good agreement with the experimental results. On this basis, the heat absorption and heat storage of the phase change process were analyzed. In the initial stage of melting, the bottom solid-phase heat storage was higher than the wall heat flux. As the liquid phase area expanded, the melting rate decreased, and the wall heat flux was basically the same as the solid phase heat storage of the PCM. After 360 s, the heat flux on the top wall and the solid-phase heat storage continued to decrease to zero. Simultaneously, simulations of paraffin/silver nanoparticle CPCM with different mass fractions showed that adding 0.5wt%~2wt% of silver nanoparticles can improve the thermal conductivity of paraffin, but the latent heat reduced. When the phase change process was over, the heat absorbed by the material was converted into sensible heat. The heat transfer on the bottom surface was reduced and energy mainly carried out through the vertical wall. Besides, the flow of the liquid phase during the melting process was analyzed. The liquid layer of the phase change material thickened, and the Nusselt number decreased and tended to stabilize. Increasing the silver nanoparticle concentration reduced the Nusselt number.