To place a muffler in a front area to make it suitable for an off-road motorcycle, A down frame extending downward obliquely from a head pipe ahead of an engine and a lower frame connected with its lower end, extending backward under the engine, are provided. A muffler is located in the vicinity of the joint between the down frame and the lower frame where its rear surface is curved forward in a convex pattern along the down frame and the lower frame. An exhaust pipe extending from a cylinder head is almost S-shaped as seen sideways and its forward curved portion and lower backward curved portion are vertically arranged with its lower end connected with a lower portion of the muffler.