Abstract: A bicycle rack for supporting bicycles in an upward standing position at the back end of a vehicle with the bicycles standing in a substantially vertical position angled horizontally at the back end of the vehicle. The trailer hitch sleeve mounted bicycle rack supports bicycles, each in an upward standing position on a center support post. The bicycle rack includes a base member (22) of which the tongue portion (23) slides into a trailer hitch sleeve (11). An adjustable sliding member (21) slides onto the base member (22). A vertical support post (20) is affixed to the sliding member (22). A series of horizontal trays (31) angled from the base of the vertical support post (20), and a series of bicycle front fork mounts (32) at the top of the vertical support post (20). The horizontal trays (31) receive a portion of the rear wheel of a bicycle so as to cradle the wheel and support the bicycle.