A pore-scale model combining the Lattice Boltzmann method (LBM) and enthalpy-based method (EBM) is established to investigate the ice melting process in porous media with or without distributed carbon particles. This model is consisted of coupled flow fluid, heat transfer and melting process and is used to study the effects of conduction and convection on the melting process. The results agree well with the analytical model. Effects of thermal diffusivity, porosity, Rayleigh number on the melting rate, temperature distribution and Nusselt number are investigated. It is found that the melting rate can be significantly promoted by decreasing the porosity of porous media under a fixed Rayleigh number, but the Rayleigh number has little effect on the melting rate in porous media except the case without carbon particles. The natural convection has insignificant effect on the temperature distribution in porous media, while the carbon particles have important effect on the temperature distribution of the porous media.