The combustion characteristics and extinction limits for the catalytic combustion of a methane/air mixture in a microtube are investigated computationally using the commercial CFD code FLUENT coupled to an external subroutine DETCHEM. The effects of the microtube dimensions, conductivities of wall materials, external heat losses and flow velocity on the combustion stability, are also studied. The numerical model is set as either adiabatic or non-adiabatic with a fixed exterior heat transfer coefficient. Numerical results indicate that thermal conductivity and wall thickness are vital to preheat the methane/air mixture through the conducting wall. Two types of extinction occur, i.e., thermal quenching and blow out. These extinction limits are characterized by wall surface temperature in the microtube and the ratio of Pt(s)/O(s).