An engine is configured so that a muffler is affixed to the exhaust opening of the cylinder, and the air-cooled cylinder is cooled by a cooling fan. The engine is provided with a muffler cover for covering the muffler, and exhaust gas is discharged inside the muffler cover along the wall surface of the muffler. A second cooling air is combined with the exhaust gas flow from the upstream side thereof to be parallel thereto, and a first cooling air having been caused to flow under the muffler is caused to perpendicularly impinge against the exhaust gas flow on the downstream side thereof. Thus, the cooling airs are combined inside the muffler cover with the exhaust gas flow, and as a result the temperature of the exhaust gas is sufficiently reduced at the time when the exhaust gas is discharged from the opening of the muffler cover to the outside.