A bicycle rack for carrying a bicycle adjacent the rear of a vehicle. The bicycle rack includes an adjustable frame assembly having a first frame member attached to a housing and a second frame member attached to a connecting member. The connecting member is rotationally coupled to the housing to allow relative pivotal movement between the first and second frame members. A locking member is disposed within the housing and selectively movable between a first position, in which the locking member engages the connecting member to impede relative rotational movement between the connecting member and the housing, and a second position, in which the locking member is disengaged from the connecting member to allow relative rotational movement between the connecting member and the housing. At least one support arm is coupled to the housing and configured for sliding and pivotal movement between a stowed position and an extended position in which the arm engages the housing to support a bicycle adjacent the vehicle. A mounting assembly is positionable on the support arm to hold the bicycle in place during travel.