This paper presents results of theoretical and experimental research concerning synthesis of multilayer asymmetric oxygen-permeable membrane and its application for partial oxidation of methane. The membrane is based on macroporous Ni-Al foam substrate with three layers of perovskite-fluorite nanocomposites with graded (meso-micro) porosity, thin dense MnFe2O4-Ce0.9Gd0.1O2 layer and porous layer of LaNi0.9Pt0.1O3/Pr0.3Ce0.35Zr0.35O2-x catalyst. Testing of membrane in methane partial oxidation process demonstrates a good and stable performance. The mathematical modeling of the methane partial oxidation process in the catalytic membrane reactor has been provided. The developed model was applied to find the process (temperature, gas flow rates, etc.) and membrane (pore diameter of porous layer, thickness of porous layer) parameters corresponding to highest methane conversion and syngas selectivity.