To conduct effective oxidization-removal of CO and HC in the exhaust gas with an exhaust emission control device, by mixing fresh air with exhaust gas properly without need for using an expensive air pump.

After a piston 4 conducts operations of ordinary four strokes of intake, compression, power, and exhaust, it sequentially-conducts a secondary intake stroke with both an intake valve 12 and an exhaust valve 13 opened without causing fuel supply and a secondary exhaust stroke with the suction valve 12 closed and the exhaust valve 13 opened. This makes it possible to obtain properly mixed gas of exhaust gas and fresh air during the second intake stroke and send it into the exhaust emission control device during the second exhaust stroke, thus it is possible to make CO and HC react to fresh air in the mixed gas quickly for effective oxidization-removal, thereby eliminating use of an air pump.