Abstract: An apparatus for cooling a cylinder head of an engine which includes a cylinder head cover in the form of a plate adapted to fully cover an upper open surface of the cylinder head, an upper wall of the cylinder head having an insert hole for inserting an ignition plug fitting and removing tool, the insert hole being formed on an inner wall thereof with an inclined guide groove for guiding the ignition plug fitting and removing tool, an oil passage formed in the cylinder head cover, one end of the oil passage being opened at a side portion of the cylinder head cover and the other end being branched such that the branched ends extend around a plug seat in the cylinder head, a recess formed around the plug seat in the cylinder head, covers covering the recesses, and nozzles each disposed between the recesses and the other end of the oil passage with one end of each nozzle connecting with the other end of the oil passage and the other end extending into an associated recess whereby lubricating oil pumped up from