ABSTRACT In present work, a local thermal non-equilibrium numerical model of low concentration methane combustion in porous media is established. The modified thermal effective thermal conductivity of foam ceramics was introduced. The heat and mass dispersion effect as well as the influence of porous media structure on the heat transfer were fully considered. Studies found that the combustion flame front of low concentration methane in porous media always show a S-shaped state under special conditions. The influencing factors of inlet velocity, methane concentration, wall heat loss, and the porous burner size were analyzed. Results show that without initial thermal perturbation and the absence of defects in the porous media, the flame front in porous burner still has the possibility of inclination. As the inclination of the flame front continues to increase, the flame keeps approaching the burner outlet until blow off. Among the considered four influencing factors, the size of porous burner has the greatest influence on the inclination of flame front. As the burner diameter increases from 0.04 m to 0.12 m, the inclination angle of the flame front increases continuously, and the maximum inclination angle is 36°. The flame inclination will cause uneven temperature distribution downstream of the burner and local heat concentration. With the increase of wall heat loss, the high-temperature zone downstream of the burner will evolve into a local high-temperature zone near the flame front. With the reducing of porous burner diameter, the inclinational instability could be suppressed to some extent.