The solid-liquid phase change process is of significant importance to the thermal energy storage and electronics cooling using phase change material. In this paper, the central moments multiple-relaxation time (CM-MRT) collision model has been introduced into the solid-liquid phase change lattice Boltzmann model, in order to solve the solid-liquid phase change problem in porous medium at pore scale. To evaluate the influences of different collision functions, the problems of one-region phase change and natural convection with phase change at pore scale have been investigated. The results have showed that the CM-MRT model possessed higher accuracy in revealing temperature and liquid fraction distribution. Compared with mesh system of 256 × 256, the CM-MRT model with 64 × 64 possess the minimum error, 0.014%. Besides, in the case of high Rayleigh number (5 × 107) and low Prandtl number (0.005), the CM-MRT model presented extraordinary stability and the clear phase interface when investigating the heat transfer of porous medium composite phase change materials at the pore scale.