To provide a transmission device for a bicycle that employs no chains and is applicable to a general chain-transmission bicycle.

A front bevel gear pair 2 has a large bevel gear 21 incorporated with a pedal shaft of a bicycle and a small bevel gear 22 rotatively meshed with the large bevel gear 21, and a rear bevel gear pair 4 has a large driven bevel gear 41 incorporated with a rear wheel shaft and a small transmission bevel gear 42 rotatively meshed with the large driven bevel gear 41. An inflective element 5 is connected to the output end of the small bevel gear 22 so as to be rotated along therewith. The front end of a rigid element 6 connected to the input end of the small transmission bevel gear 42 and the rear end of the inflective element 5 connected to the front bevel gear pair are connected so as to be rotated together. A rotation by pedaling provides mutual rotations between the front bevel gear pair 2, the rear bevel gear pair 4, and the inflective and rigid elements 5 and 6 connected between them to thus rotate the rear wheel and then drive the bicycle forward.