Premixed combustion in a porous medium burner is investigated numerically. A two-dimensional steady, laminar flow model is used. A single-step reaction of methane is used for the chemical kinetic model. The model also includes thermal radiation transport of the porous media that is placed inside the burner. The radiative transport equation is solved by using the discrete ordinate method. The results show that, for each equivalence ratio, the flame can be stabilized at various axial locations with different flame speeds. The flame temperature increases with the equivalence ratio and flame speed. Furthermore, the energy release rates are much higher than that of a free flame for the same equivalence ratio as a result of higher flame speed.