The steam reforming of methane with addition of a small amount of oxygen was simulated in a co-current, isothermal and plug-flow-type membrane reactor with selective permeation of hydrogen. The effect of operating conditions on the conversion of methane and the permeated hydrogen yield was investigated using two dimensionless numbers, the Damkohler number and the permeation number, theta. Methane conversion, X-CH4, shows approximately the same dependency on permeation number in terms of the permeability ratio of hydrogen to nitrogen, while hydrogen purity in the permeate increased with an increase in hydrogen selectivity. As for heat balance of the membrane reactor, the addition of oxygen, which generates heat of combustion, in feed at O/C of 0.3 to the endothermic steam-reforming reaction, is required to maintain the membrane reactor autothermal. For the case of heat-balance of membrane reactor system, which considers the heat balance of the membrane reactor and the heat of combustion of the retentate stream, the system can be autothermal for the case of methane conversion of 0.7-0.8.