The present invention has an object to more enhance the efficiency of the purification of the CO-containing exhaust gases with a catalytic-component-supporting type catalyst, particularly, to enable both achievement of high purification efficiency and long-term stable maintenance of high purification efficiency without increasing the quantity of the catalytic component as supported. As a means of achieving this object, a process for purification of exhaust gases, according to the present invention, is a process for purification of exhaust gases to remove CO therefrom, and is characterized by comprising the step of bringing the exhaust gases into contact with a catalyst layer at a temperature of 250 to 600.degree. C., a pressure drop of not more than 100 mmH.sub.2O, and a linear velocity of 0.5 to 10 m/s, wherein the catalyst layer includes a honeycomb-structural catalyst having an opening size of 1.0 to 3.0 mm, an opening ratio of 60 to 80%, and an inner wall thickness of less than 2 mm.