PURPOSE: To restrain variations in the air-fuel ratio, by dividing the operating range of feed-back control into a plurality of sub-ranges so that the feed-back control is initiated when the operating range is shifted, in accordance with the coefficient value of the objective range.

CONSTITUTION: In an air-fuel ratio feed-back control operating range, a basic fuel injection time which is obtained by an ECU5 in accordance with the outputs of a rotating angle sensor 11 and an intake-air pressure sensor 8, is compensated in accordance with a compensating coefficient, etc. obtained from the output of an O2 sensor 15 so that the injection time of a fuel injection valve 6 is controlled. In this stage, the above-mentioned operating range is divided into a plurality of sub-ranges, and the averaged value of the above-mentioned compensating coefficients is calculated and memorized when the operating range is in the O2 sensor feed-back control operating range. When the operating range is shifted from the first range (idle operation range) to the O2 sensor feed-back operating range, control is made such that the air-fuel ratio feed-back control is initiated with the use of the above-mentioned averaged value as a compensating value.