Methane in a feedstock gas having methane as its main component, is partially oxidized with oxygen, which selectively permeates from a first side to a second side of a oxygen selective permeation ceramic membrane. Air is contacted with the first side of the oxygen selective permeation ceramic membrane, and the feedstock gas containing methane is contacted with the second side of the oxygen selective permeation ceramic membrane. A first catalyst for partial oxidation of methane is disposed two-dimensionally on the second side of the oxygen selective permeation ceramic membrane, and a second catalyst for partial oxidation of methane is disposed three-dimensionally in the feedstock gas stream downstream from the first catalyst. Furthermore, steam is mixed into the feedstock gas stream at a ratio of 0.25 to 0.5 moles of steam based on the moles of carbon in the feedstock gas.