Air-fuel ratio control system for internal combustion engine

An air-fuel ratio control system for an internal combustion engine provided with a NOx trap catalyst which is disposed in an exhaust gas passageway and arranged to trap NOx when the air-fuel ratio of exhaust gas flowing to the NOx trap catalyst is lean and to release and reduce trapped NOx when the air-fuel ratio is rich. The air-fuel ratio control system comprises a sensor for detecting an air-fuel ratio of exhaust gas in the exhaust gas passageway downstream of the NOx trap catalyst. Additionally, a control circuit is provided and configured to cause the engine to operate at a rich air-fuel ratio to accomplish a rich air-fuel ratio engine operation after an engine operation at a lean air-fuel ratio, and continue the rich air-fuel ratio engine operation for a duration even after the sensor has detected that the air-fuel ratio of exhaust gas is rich.