A front end portion of a rear swing arm of a motorcycle is pivoted to a vehicle body frame via a rear swing-arm bracket. A rear wheel is rotatably supported by a rear end portion of the rear swing arm. The rear swing arm is provided with a shaft drive mechanism for driving the rear wheel. The rear swing-arm bracket includes a left/right pair of frame members, cross members and a connection portion. A front end portion of the shaft drive mechanism faces a right-side opening at a position biased towards the frame member. The connection portion is extendedly provided at a position biased toward the center line (the center) extending along the longitudinal direction of the vehicle. The front end portion of the rear swing arm is fastened to the frame member and the connection portion via a pivot shaft and a nut in a left-side opening.