A collapsible bicycle rack to be transported at the rear of a motor vehicle for carrying bicycles that are aligned vertically with their front wheels facing up. The bicycle rack includes an upper front wheel support having stationary front wheel holders and oppositely-aligned adjustable front wheel holders that can be moved relative to the stationary front wheel holders to vary the distance therebetween in order to support the front wheels of bicycles having different diameters. The bicycle rack also includes a lower rear wheel support that rotates simultaneously with the upper front wheel support between an unfolded deployed configuration extending outwardly from an upstanding main support bar and a collapsed compact configuration lying adjacent the upstanding main support bar.