To examine the effect of so-called "concentration polarization" on the performance of a membrane reactor with a highly hydrogen-permeable membrane, methane steam reforming was conducted, using a Pd/Ag membrane with a thickness of a few micrometers. First, the relation between the methane conversion and the hydrogen recovery was experimentally examined, and the relation was compared with that predicted by a rather simple simulation that assumes the instant achievement of equilibrium. When the hydrogen recovery was smallest, the experimental results agreed well with the simulation results. With increasing reaction pressure, the experimental methane conversion became lower than the simulated conversion. These results suggest that the reaction is limited by reduced hydrogen removal, because of the concentration polarization. The influence of concentration polarization was confirmed by the comparison of the experimental results of hydrogen permeation from a mixture of H-2 and N-2 with the simulation results based on the plug-flow model. It then was experimentally attempted to reduce the concentration polarization by changing the configuration of the reactor. The methane conversion was successfully improved using reactors that had narrower inner diameters and baffle plates, probably because of the reduction in concentration polarization. It was concluded that the reactor configuration was quite essential to make the best use of a membrane reactor with a highly permeable membrane.