An automatically stoppable internal combustion engine comprises an exhaust purification catalyst, an upstream side air-fuel ratio sensor, a downstream side air-fuel ratio sensor, and sensor heaters heating air-fuel ratio sensors. A controller comprises an air-fuel ratio control part and a heating control part. The heating control part controls the temperature of the upstream side air-fuel ratio sensor to the activation temperature or more and the temperature of the downstream side air-fuel ratio sensor to less than the activation temperature during automatic stop of the internal combustion engine. The air-fuel ratio control part controls the air-fuel ratio of the exhaust gas based on the outputs of the two air-fuel ratio sensors during engine operation and controls the air-fuel ratio of the exhaust gas temporarily based on the output of the upstream side air-fuel ratio sensor without using the output of the downstream side air-fuel ratio sensor.