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, including a plurality of valve-driving apparatuses provided for driving valves of different cylinders of the internal combustion engine, wherein each valve-driving apparatus includes an electrical motor as a driving source for generating rotation motion; and a power transmission mechanism for converting the rotation motion of the electric motor into opening and closing motion of the valve to be driven and for transmitting the opening and closing motion to the valve through a cam or a link.