To lessen the limitations in layout of various pieces of equipment for an engine cooling system arranged about an engine and reduce the weight and cost of the cooling system by shortening its cooling water return pipe.

A cylinder head 6 and a chain cover 21 are formed with cooling water outlet ports 28 and 29 so that the outlet for the cooling water that has higher temperature after cooling the cylinder head 6 and the cylinder block leads to a radiator-side water jacket 27 defined in the cylinder head 6, which outlet ports are connected to the cooling water inlet in the radiator by means of a cooling water return pipe 25. That arrangement shortens the return pipe 25, which is laid between the radiator and the chain cover 21, to lessen the limitations in layout of various pieces of equipment arranged around the engine. Shortening the return pipe also contributes to its lighter weight and smaller cost.