PURPOSE: To accurately detect an air-fuel ratio by branching a bypass passage on which an adsorption device is arranged from an exhaust passage, providing a catalyst device and a secondary air supply device to the catalyst in the lower course of the branch portion, and feedback-controlling an engine air-fuel ratio to be a target value based on the air-fuel ratio which is detected by an air-fuel ratio detecting means.

CONSTITUTION: A bypass passage 3 on which an adsorption device 4 is arranged is branched from an exhaust passage 2. A first temperature sensor 9 is arranged upstream from an exhaust selector valve 8, while a second oxygen sensor 10 as an air-fuel ratio detection means is arranged downstream from the adsorption device 4. When a temperature detected by an adsorbent temperature sensor 7 is not higher than a heat-resistant temperature, exhaust is circulated to the bypass passage 3 to adsorb and separate combustible components. When a cooling water temperature exceeds a set value for low temperature, an air-fuel ratio is brought under feedback-control based on a signal from the second oxygen sensor 10. When the combustible components are separated from the adsorption device 4, the air-fuel ratio at the separation time can be detected by the second oxygen sensor 10. The air-fuel ratio to a catalyst device 5 is accurately kept.