Engine cooling structure directs cooling air, introduced into a case by operation of a fan, to a cylinder block of an engine and then discharges the cooling air out of the case through an outlet port along meandering flow passages. Case cooling structure directs cooling along the inner surface of the case. Further cooling flow passage directs the air to vertically-oriented heat radiating fins so that the cooling air flows upward along the fins and then is discharged through the outlet port. Metal cooling-fan cover is supported by the lower cover via mounting members, and a resin-made cover guide is fastened to the engine together with supporting portions and interposed between the fan cover and the engine.