PURPOSE: To prevent engine stall and hunting, by obtaining the engine speed used for judging fuel cut and resetting of fuel cut from the rate of change of the engine speed in a method of cutting fuel supply at the time of deceleration.

CONSTITUTION: The rate of change ΔN of the engine speed is used, for instance, for determining the fuel cut level. Here, a maximum engine speed ND is selected in case of ΔN≥ΔN3 while a medium engine speed NE is used in case of ΔN3> N>ΔN4. Further, a maximum engine speed NF is selected in case of ΔN4≥ ΔN. That is, the higher the rate of change ΔN of the engine speed, the fuel cut level is lowered and the reset level is raised. By employing such a method, it is enabled to prevent stall and hunting of an engine.