A valve-driving system, which is applied to an internal combustion engine having a plurality of cylinders, for driving an intake or exhaust valve provided in each cylinder, comprising: a plurality of valve-driving apparatuses, each of which is provided for at least each one of the intake valve and the exhaust valve, each valve-driving apparatus having an electrical motor as a driving source for generating rotation motion and a power transmission mechanism provided with a transmitting section for transmitting the rotation motion generated by the electrical motor and a converting section for converting the rotation motion transmitted from the transmitting section into opening and closing motion of the valve to be driven; and a motor control device which controls operations of electric motors of the respective valve-driving apparatuses in accordance with the operation state of the internal combustion engine.