In a system, an angle sensor outputs a pulse each time an output shaft of an internal combustion engine rotates by a preset angle, and a calculator calculates speed-change information indicative of a change in a speed of rotation of the output shaft based on the pulses outputted from the angle sensor. A determiner determines, based on the speed-change information, whether at least one of the pulses outputted from the angle sensor represents a proper timing for a preset of a pinion of a starter with a ring gear mounted on the output shaft. A pinion engaging unit shifts the pinion toward the ring gear so that the pinion is engaged with the ring gear when it is determined that the at least one of the pulses outputted from the angle sensor represents the proper timing for the preset of the pinion with the ring gear.