A reforming reactor, particularly for the water vapor reforming of methanol, with three serially arranged reactor steps, each of which is charged with a catalyst pellet fill. According to the invention, the center reactor step is maintained at a temperature which is suitable for the reforming reaction, while the two other reactor steps remain unheated. The present invention may be used as a reforming reactor for the water vapor reforming of methanol for the purpose of producing hydrogen in a fuel-cell operated motor vehicle.