A clutch control method is used in a vehicle that has a dog clutch and an engagement sensor, which detects an engagement of a dog clutch. The clutch control method includes executing an engagement of the dog clutch when a magnitude of a differential rotation of the dog clutch is less than or equal to a prescribed value when the engagement sensor is normal and then determining the engagement of the dog clutch using the engagement sensor. The clutch control method further includes setting the differential rotation of the dog clutch to a value larger than the prescribed value when the engagement sensor has failed and then determining the engagement of the dog clutch based on a difference between the differential rotation of the dog clutch at a time of starting the engagement of the dog clutch and the differential rotation of the dog clutch.