To provide an engine head structure for “omission or shortening a fuel pipe that withstands a high pressure”, “simplification or omission of a support bracket for a fuel accumulator and/or a fuel injection device”, “reduction of the number of parts” by devising a fuel accumulator and a support structure therefor, and the like. An engine head structure has a support bracket for mounting a fuel accumulator including a joining portion with a fuel injection device on a cylinder head, is disposed on a side of the fuel injection device or between adjacent fuel injection devices. The support bracket includes a member having a mounting portion on which the fuel accumulator is placed and mounted, a mounting leg portion extending from the mounting portion and mounted on the cylinder head, and an aligning leg portion extending from the mounting portion for positioning the support bracket with respect to the cylinder head.