In an engine starter of the present invention, a driving shaft to output a rotating force and a crankshaft of an engine are linked continuously. The engine starter comprises a one-way clutch to prevent an overrun of an armature after the engine starts. In the one-way clutch, a connecting rotation number in which an inner ring and an outer ring change from a disconnected state to a connected state in a decreasing process of engine revolutions is set above a lower limit of the engine revolutions above which the engine under suspension of the fuel supply is able to get restarted by itself by resuming of fuel supply. Therefore, the engine is always able to get restarted quickly even in a low-rotation range.