PURPOSE: To improve controlability, when air-fuel ratio feed-back control is carried out by an oxygen sensor, by changing proportion and integration constants within a predetermined time after the sensor output shifts to either lean or excessively rich one and while said output does not shift again to same.

CONSTITUTION: A control unit 10 controls the duty ratio of a solenoid valve 13 for a carbureter 12 according to the output of an oxygen sensor 4 upstream of a ternary catalyzer 5 so that air-fuel ratio is feed-back controlled. While proportion and integration constants in the feed-back control need to be changed according to the running condition, said constants are changed within a predetermined time after the running conditions of an engine shift from the lean or excessively rich condition of air-fuel ratio to the reverse one and when said air-fuel ratio does not shift again to the reverse condition.