A bicycle rack for transporting, in upright position, one or a plurality of bicycles and having a base provided with a pair of spaced-apart base members with provision for attachment to a part of a vehicle or other supporting surface and with elongate upwardly open channel members mounted to the base in transversely extending relation to the base members to receive both wheels of a bicycle in one of the channel members and with the continuity thereof permitting rolling of a bicycle therealong as the bicycle is mounted in upright position on the rack. A frame member of a generally inverted U-shape extends upwardly from the base and has a pair of legs associated one with each of the base members and carrying a pair of clamp members extending from opposite sides thereof toward a position to have a clamp device on the end of each clamp member engage a part of a bicycle frame and hold the bicycle securely in position and as supported by the channel member.