A transmission apparatus for a bicycle is capable of performing a transmission operation even while operating or running by the inertia of the bicycle. The transmission apparatus T for a bicycle includes a driving sprocket member rotationally driven by a crankshaft; a multi-stage driven sprocket member drivingly connected to the output shaft cooperatively engaged and rotated with the rear wheel; a chain applied over the driving sprocket member and the driven sprocket member; and a transmission changing-over mechanism M2 for positioning the chain among a plurality of transmission sprockets. The driven sprocket member is integrally arranged to always be rotated, and the one-way clutch for transmitting a rotation of the crankshaft to the driving sprocket member while in its normal rotating direction is arranged in the power transmitting path extending from the crankshaft to the driving sprocket member.