Engine starting performance is enhanced by a brushless motor having no rotor position detecting sensor. In the first place an engine is rotated forward and then is reversely rotated to overcome a high load region of the engine. Then, the engine is accelerated and rotated forward and started. In a light load region of the engine, the engine is immediately accelerated and normally rotated. It is judged whether the region of the engine is the high load region or light load region based on the rotation speed when the starting operation is started. After the starting operation is started, if the forward rotation speed reaches a first speed, and a second speed which is higher than the first speed is obtained even after predetermined time is elapsed, an immediate starting-judging section 36 outputs a detection signal to a starting/normal rotation control section 37.