A method is provided for refining an argon gas, in which oxygen is added to the argon gas containing hydrogen, carbon monoxide (CO), and oxygen as impurities so that the hydrogen and the CO are converted into water and carbon dioxide in a catalyst tower, or hydrogen is added to the argon gas so that the oxygen is converted into the water; the method including: monitoring the hydrogen, the CO, and the oxygen on an outlet side of the catalyst tower; and at least one of adding the oxygen to the argon gas when any one of the hydrogen and the CO is detected on the outlet side of the catalyst tower, and adding the hydrogen when the oxygen is detected, wherein the oxygen or the hydrogen to be added is intermittently added to the catalyst tower relative to continuous supply of the argon gas to the catalyst tower.