A bicycle includes a frame, and a transmission device including a motor, a transmission unit, a crank unit, a sprocket and a unidirectional bearing. The transmission unit includes a first gear driven by the motor, a one-way clutch mounted in a compartment of the frame and connected between the first gear and the motor for limiting rotation to be transmitted from the motor to the first gear, and a second gear meshing with the first gear. The crank unit includes a crank shaft extending into the second gear, and first and second cranks connected respectively to two ends of the crank shaft. The sprocket is formed with an engaging hole non-rotatably engages the second gear and a receiving groove receives the unidirectional bearing for driving rotation of the sprocket in a single direction.