PURPOSE: To maintain purifying property of a catalyst, by controlling an injection quantity of fuel by an air-fuel feedback correction coefficient obtained in accordance with the concentration of a specific component in exhaust gas while controlling amplitude of the correction coefficient and its frequency in accordance with a detected flow of intake air.

CONSTITUTION: A control device, while it is in feedback control, reads input data corresponding to the output of an O2 sensor 20 from a random access memory (RAM) 48 to be compared with a reference value, setting a rich flag to 1 when air-fuel ratio is in a rich side for the theoretical value while to 0 when the air-fuel ratio is in a lean side. Next the device, immediately after the flag is set to 0 from 1 or reversely inverted to be set, inputs a fixed value R to X for increasing a change quantity of a correction coefficient FAF, while the device, if the flag is not immediately after being inverted, reads input data of an intake air flow Q from the RAM48, obtaining an integration constant K in accordance with Q to be input to X. Next the device, calculating FAF← FAF-X in case of the flag being 1 while FAF←FAF+X in case of the flag being 0, stores the obtained FAF in the RAM48. That is, exhaust gas is purified by controlling the integration constant K of the correction coefficient FAF in accordance with the intake air quantity Q.