A cover structure, for an internal combustion engine, that can inhibit lubricating oil from remaining at a protrusion portion is provided. The cover structure for an engine includes a chain case that covers a timing train mechanism, and a timing train chamber is formed between the chain case and the engine main body. The chain case includes bolt insertion holes provided at side marginal portions and directed toward the engine main body, a variable-valve boss portion and a second-oil-path boss portion that protrude from a wall portion toward the engine main body and form a recessed portion where lubricating oil for lubricating the timing train mechanism remains, and a first rib that is protruding from the wall portion toward the engine main body and provided upper than at least the recessed portion.