A vehicle includes an internal combustion engine, an air-fuel ratio sensor provided in an exhaust passage of the internal combustion engine, and a controller. The controller is configured to diagnose a responsiveness of the air-fuel ratio sensor on the basis of an output voltage of the air-fuel ratio sensor in a predefined period. The period is a period over which exhaust gas goes through the air-fuel ratio sensor during the internal combustion engine is rotating without fuel injection.