A motorcycle in which a front end portion of a rear swing arm for rotatably supporting a rear wheel is swingably supported via a supporting shaft by an engine supported by a body frame. The rigidity of a rear swing arm is enhanced without increasing the weights of the supporting shaft and the like. Upper end portions of a pair of right and left bracket are fixed to both ends of a supporting shaft. A cross-pipe connects lower end portions of the brackets and is fixed to the engine at a position under the supporting shaft. A pair of right and left rotatably supporting portions are swingably supported by the supporting shaft at positions between the brackets and the engine.