The present invention relates to a device for driving a sprocket of a bicycle, which enables a rider to easily rotate both pedals even with little force when both cranks of the pedal are vertically positioned. According to the present invention, when a crank (11) gets to be vertically positioned by rotating the pedals (11a), a guide pin (21) projected from a rotating plate (20) draws a tensile spring (41) from the guide groove (31) and thereby the rotating plate (20) gets to be elastically rotated so the crank (11) can go off the vertical position rapidly. Accordingly, the rider can easily rotate the pedals, and at the same time, the force of restitution of the drawn tension spring (41) can help the sprocket (10) be rotated. Consequently, the accumulated force of the tensile spring (41) accelerates the rotation of the sprocket (10) to enable the crank (11) to go off the vertical position effectively, which in turn enables the rider to drive the bicycle with ease.