PURPOSE: To prevent abrupt change in power by estimating a decelerated condition and then maintaining an injection ratio represented by quantity or period for a certain interval from the cutting-off starting point of fuel supply to its completion that a misfire will not occur and the quantity of the injection may be made slightly more than that of the injector's irregular injection.

CONSTITUTION: A computer 5 estimates the decelerated condition on the criteria that an idle switch 2 is on, an engine speed is decelerated and the engine speed is lower than a fixed value at which fuel is to be cut off. Fuel cut-off based on the estimation is performed in such a manner that injection is maintained at a present ratio τn represented by quantity or period for a certain interval Tc from the estimation point To, if the τn is lower than the minimum capacity τmin of an injector, injection is executed at a ratio τm which is provided as a function of the engine speed for an interval (Tc-Tm), and injection is executed at a ratio τn and the fuel is then completely cut off. In another case of (τn=τmin) fuel is injected at a rate τn during a certain interval Tm before fuel in cut-off. Since an abrupt change in power and fluctuation in pulses will not occur, a shock or a surge of the vehicle may be prevented.