The heterogeneous oxidation of methane-air mixture in a honeycomb catalytic reactor is investigated numerically in the present study. An improved multi-step surface reaction mechanism for methane oxidation on platinum is proposed so that surface ignition of lean methane-air mixtures is better modeled. First, this surface mechanism is used to determine the apparent activation energy of methane-air catalytic combustion. The predicted activation energies are found to agree well with the experimental data by Trimm and Lam (1980) and by Griffin and Pfefferle (1990). The chemical model indicates that, depending on the surface temperature, the surface reaction rate is dominated by either the oxygen desorption rate or by the methane adsorption rate.