PURPOSE: To restrain the generation of NOx in particular, by enriching the air- fuel ratio of an engine in its feed-back control range when the engine is shifted into the feed-back control range from the other range, so that the feed-back control of the engine is initiated.

CONSTITUTION: Upon operation of an engine an ECU receives outputs signals from a throttle valve opening degree sensor 4, an intake-air pressure sensor 8, a water temperature sensor 10, a rotating angle sensor 11, an O2 sensor 15, etc., and judges whether the engine is in an air-fuel ratio feed-back control operation range or not. If it is in the feed-back control operation range, the ECU calculates the averaged value of compensating coefficients which varies in accordance with the output of the O2 sensor 15, and memorizes. Meanwhile, when the operating condition of the engine shifts into the feed-back control operation range from the other ranges, the feed-back control in the shifted range is initiated with the use of the value, as a compensating coefficient, which is obtained by multiplying a predetermined value by or adding the same to the above-mentioned averaged value of compensating coefficients, thereby the air-fuel ratio is made rich.