In a motorcycle, a pivot plate on a drive shaft side is arranged closer to a vehicle body center axis side than the drive shaft and, at the same time, a swing arm mounting portion of the pivot plate in the vicinity of the drive shaft is flattened. Further, a lower cross pipe is extended between the left and right pivot plates in a state that the lower cross pipe projects from the pivot plate on the drive shaft side, a down tube is lowered from a head pipe, a lower pipe is extended rearwardly in the longitudinal direction of a vehicle body frame from a lower end of the down tube, and a rear end of the lower pipe is connected to a projecting portion of the lower cross pipe thus offsetting the pivot plate arranged closer to the drive shaft side than the lower pipe to the vehicle body center axis side.