PURPOSE: To make it possible to enhance fuel mileage in all operating conditions by carrying out in such a manner that fuel is cut off upon deceleration other than during idling but is not cut off just after cranking.

CONSTITUTION: When a vacuum switch 10 issues a low level signal and the engine speed exceeds a set value, an OR circuit OR3 delivers a low level signal so that a solenoid valve 6 is not energized, that is, when the engine speed exceeds a predetermined value upon idling, fuel supply is cut off. Further, when a universal pressure switch 20 issues a low output signal and a delay circuit D also issues a low output signal with the result of that a strater switch is turned off, an OR circuit OR1 delivers a low level signal, and further, when the engine speed exceeds the predetermined value, an OR circuit OR2 issues a low level signal, that is, fuel is cut-off when the engine speed exceeds the predetermined value upon engine deceleration other than during idling. Further, fuel is not cut off just after cranking due to the provision of the delay circuit.