The steam reformer has a double-cylinder structure having an inner cylinder and an outer cylinder surrounding the inner cylinder. The inner cylinder contains a high-temperature reaction section and an adjacent section being adjacent to the high-temperature reaction section. The high-temperature reaction section contains a mixed-catalyst bed prepared by mixing a steam reforming catalyst and an oxidation catalyst, and an oxygen-containing gas introduction section. A heat transfer suppresser is structured to suppress heat transfer from the high-temperature reaction section to the adjacent section or to the oxygen-containing gas introduction section. With the heat-transfer suppressor, the thermal diffusion from the high-temperature reaction section to peripheral area is effectively suppressed.