Abstract: A bicycle rack for holding a bicycle in an upright position and designed to be attached to the luggage carrier on a motor vehicle. The rack includes a frame bracket with a jaw with an upwardly facing jaw which receives the crank assembly housing of the bicycle. The jaw preferably includes a fixed member and a movable member which moves arcuately with respect to the fixed member from an open position, to permit the bicycle crank assembly housing to be placed therein to a closed position which secures the housing from removal. A lever can be provided for such a multi-member jaw to facilitate the opening and closing thereof, and a lock may be incorporated into this lever to make the rack resistant to the theft of a bicycle therefrom and to prevent the accidental opening of the jaw during the transportation of a bicycle.