A rack for holding a bicycle by either its front or back wheel in an upright position on a floor. The rack includes a bracket which is adapted to be fitted on an elongate support frame. A rotatable lower brace extends outwardly from the bracket and includes spaced-apart arms which terminate in a downwardly extending lip. An upper brace extends generally upwardly from the bracket and includes spaced-apart arms. A bicycle is held on the rack by rolling the bicycle wheel directly into the lip of the lower brace and into and between the arms of the upper and lower braces respectively. A plurality of racks can be slidingly fitted onto a single support frame for holding a plurality of bicycles in spaced-apart relationship.