A two-cycle internal combustion engine comprises a cylinder head having an intake port and exhaust port opened to a combustion chamber, to which compressed fresh air is introduced via an intake valve. An inclined concavity is formed on a top face of a piston. An exhaust valve is opened earlier than the intake valve when the speed of the downward movement of the piston is relatively high, so that a part of exhaust gas in the exhaust port flows back to the combustion chamber in that condition. An exhaust gas swirl rotating around a cylinder axis is formed when the exhaust gas flows back and the fresh air is slowly introduced onto the exhaust gas swirl in that condition. The inclined concavity serves to smoothly guide the exhaust swirl.