To permit reliable occurrence of initial combustion at the start of an engine during which a stroke is not determined by only a crank pulse and to increase an engine speed. During a period from when cranking is started until a stroke is detected, fuel is injected once every rotation of a crankshaft before an intake stroke (or an expansion stroke), and ignition is effected once every rotation of the crankshaft in the vicinity of the top dead center, thereby enabling initial combustion without involvement of reverse rotation of the engine. If a stroke is detected, fuel injection and ignition are effected once per cycle. When the engine speed fails to become equal to or higher than a predetermined speed, the ignition timing is set to a point before the compression dead center and in the vicinity of 10 toward advance, thereby immediately increasing the engine speed. Stroke detection is permitted when the engine speed has become equal to or higher than the predetermined speed, so that the engine speed becomes stable.