Gas filtration combustion in porous media differs substantially from the combustion with free flame. A one-dimensional model is proposed, and a perturbation theory is used for the combustion front velocity analysis of the methane-air premixed combustion in an inert packed bed, The temperature distribution is predicted for either fully-developed or transient combustion state, based on direct solution and Green's function method. Finally, computational experiments are given and the results are satisfactory.