Method and apparatus for cooling the cylinder head (10) of an engine (702) of the type in which oil is delivered to the area located above the combustion chambers (32, 34, 36, 38) in the cylinder head and the latter is cooled by thus delivered oil. Oil introducing means through which oil is introduced into the area located above the combustion chambers in the cylinder head are disposed in the vicinity of ignition plug fitting bosses (54) on the cylinder head whereby oil pumped up from the oil supplying devide (700) is delivered to the area located above the combustion chambers in the cylinder head through the oil introducing means.