A valve-driving system for an internal combustion engine is provided with: an electric motor for generating a rotational driving force to drive a valve for intake or exhaust mounted on a cylinder in the internal combustion engine so as to open and close the valve in synchronization with a piston motion in the internal combustion engine; a transmitting device capable of changing between (i) a first condition to transmit therethrough the rotational driving force to the valve from said electric motor and (ii) a second condition to stop an opening or closing operation of the valve or to make the valve driven by a low lift amount; a judging device for judging whether or not synchronization between the opening or closing operation of the valve and the piston motion is abnormal; and a fail-safe device for changing said transmitting device to the second condition if it is judged by the judging device that the synchronization is abnormal.