A controller for controlling an air-fuel ratio of an engine is provided. An exhaust gas sensor is provided between an upstream catalyst disposed upstream of an exhaust pipe and a downstream catalyst disposed downstream of the exhaust pipe. A virtual exhaust gas sensor is configured downstream of the downstream catalyst. After an operating state in which the air-fuel is lean is cancelled, or after a fuel cut is cancelled, an estimated output of the virtual exhaust gas sensor is estimated based on a gas amount that contributes to reduction of the upstream and downstream catalysts and a detected output of the exhaust gas sensor provided between the upstream and downstream catalysts. The air-fuel ratio of the engine is controlled in accordance with the estimated output of the virtual exhaust gas sensor. Thus, the catalyst converter is appropriately reduced in accordance with a load of the engine and a state of the catalyst. When the reduction process is completed, an adaptive air-fuel ratio control based on the output of the exhaust gas sensor is started.