A carbon monoxide converter whose catalyst temperatures can be precisely controlled even under a high load. The carbon monoxide converter includes shift catalyst beds arranged in tandem for conducting a shift reaction for converting CO and H.sub.2O to H.sub.2 and CO.sub.2. The shift catalyst beds are arranged in a gas flow direction such that they are shorter on the upstream side, on which a gas containing CO and H.sub.2O is introduced, and longer on the downstream side, on which a gas containing the produced H.sub.2 and CO.sub.2 is discharged. A heat exchanger is disposed upstream of each shift catalyst bed, and the temperatures of the shift catalyst beds are controlled during the shift reaction. A gas containing CO.sub.2 and H.sub.2O discharged from the carbon monoxide converter is introduced into a carbon-monoxide-oxidizing unit.