A composite bicycle frame containing a hollow slanted-Y-shaped front frame portion, a hollow upper support paw and a hollow lower support paw. The hollow slanted-Y-shaped front frame portion comprises: (1) a generally common junction; (2) a main tube connected between the front fork assembly of the bicycle and a middle portion of the common junction in a slanted manner; (3) an upper branch tube connected between the seat assembly of the bicycle and an upper portion of the common junction in a slanted manner; and (4) a lower branch tube connected between the pedal support assembly of the bicycle and a lower portion of the common junction in a slanted manner. The hollow upper support paw is connected between the seat assembly and the rear wheel shaft assembly of the bicycle, and the hollow lower support paw connected between the pedal support assembly and the rear wheel shaft assembly. A set of generally hollow front, seat tube and bottom bracket junctions are provided for connecting, respectively, (1) between the hollow main tube and the head tube, (2) among the hollow upper branch tube, the seat tube sleeve, and the upper support paw, and (3) among the hollow lower branch tube, the bottom bracket tube, and the lower support paw. Each of the hollow tubes, paws, and junctions comprises at least a fibrous material impregnated with a synthetic resin, and these tubes, paws, and junctions are integrally united by overlapping edges of the resin impregnated fibrous material. The upper support paw and the lower support paw are connected to the rear wheel assembly at opposite sides thereof, with the upper support paw being disposed at the same side as the drive chain of the bicycle. This allows great flexibility to be obtained in designing bicycle chain related components, such as the crank set assembly and the rear derailleur assembly.