A controller is configured to execute a dither control process of operating fuel injection valves such that at least one of cylinders is a lean combustion cylinder, in which the air-fuel ratio is leaner than the stoichiometric air-fuel ratio, and at least another one of the cylinders is a rich combustion cylinder, in which the air-fuel ratio is richer than the stoichiometric air-fuel ratio, and a limiting process of limiting the dither control process such that the difference in the air-fuel ratio between the cylinders is smaller in a change period, in which a gear ratio of the multi-speed transmission is changed, than in periods except for the change period.