An internal-combustion-engine automatic stop and restart system performs restarting control by making the pinion pushing unit push out the pinion gear so as to engage with the ring gear, when the restarting condition is satisfied in a time period from a time when the automatic stopping condition is satisfied to a time when the rotation of the internal combustion engine stops. A throttle valve control unit opens the throttle valve even when the restarting condition has not been satisfied and stops control of the throttle valve in a time period from when the rotation of the internal combustion engine stops to when the restarting condition is satisfied, when the rotation speed of the internal combustion engine becomes lower than a predetermined value in a time period from when the automatic stopping condition is satisfied to when the rotation of the internal combustion engine stops.