Controller for internal combustion engine

A controller for an internal combustion engine mounted on a vehicle, wherein the engine includes an exhaust passage provided with a catalyst, the controller comprising:

• a processor, wherein the processor is configured to
• perform an auto-stopping process on the engine when the engine is idling,
• perform an auto-restarting process on the engine when the engine is automatically stopped,
• correct an amount of fuel injected into the engine so that the fuel injection amount of the engine is increased by a correction amount after the auto-restarting process is started, and
• change the correction amount in accordance with changes in an air-fuel ratio of an air-fuel mixture, which is supplied to the engine, and changes in a fuel injection amount during a period between when a fuel cut is terminated and when the auto-stopping process is started.