A bicycle includes a rear wheel rotatably mounted on a bicycle frame for rolling on a ground surface, a support unit pivotably mounted on the bicycle frame, and a locking unit disposed to releasably retain the support unit in a traveling position. The support unit includes a pivoted end, a shank member which extends from the pivoted end, and an elongated rail member connected to the shank member. The rail member has a supporting surface such that in a suspending position, the supporting surface is rested on the ground surface to suspend the rear wheel from the ground surface, and that when the support unit is turned to the traveling position, the rail member is turned to have the supporting surface face upwardly to serve as a rear rack of the bicycle.