A two-dimensional unstoady-state heterogeneous model has been developed to simulate an oxygen permeable membrane (CH4) reactor for partial oxidation of methane (POM) with steam added. The model covers all aspects of major chemical kinetics, heat and mass transfer phenomena in the tubular reactor with oxygen permeation in radial direction through an ion-conducting membrane. The temperature and concentrations of the major species in the membrane tube (catalyst bed) and air region were calculated. Results showed that radial oxygen permeation would cause a little maldistribution of gas concentrations in the radial direction of the reactor under study. The overall performance of the reactor was found to be closely dependent on its feeding and operating conditions. Improved performance in terms of high methane (CH4) conversion, high hydrogen (H-2) yield and low carbon monoxide (CO) concentration can be achieved when the reactor operates at inlet gas temperature from 900 K to 1000 K, water to fuel (W/F) ratio of round two and gas hour space velocity of about 20000/h.