In a cylinder head structure of an engine, a structure of an oil passage is simplified to downside the engine and to provide proper flow of cooling water in the cylinder head. A partition wall is disposed in the cylinder head to separate an upward valve operating chamber from a downward water jacket. A boss section is formed at a position lower than the partition wall in an edge wall of the cylinder head, and has one end joined to a chain case and the other end protruding into the water jacket. A branch oil passage is formed in the boss section. The branch oil passage has a valve upstream-side passage section specified by a section toward the chain case with respect to a junction with a cylinder head-side oil passage. The linear communication passage section communicates between an end portion of the branch oil passage protruding into the water jacket and a camshaft cap coupling surface of a second camshaft bearing section.