To provide a dog clutch for an automatic transmission in which spline teeth of a sleeve can plunge into a clutch groove at proper timing so that the sleeve is not flipped up at a shift operation.

Timing at which the spline teeth 26b1 can plunge into the clutch groove 23e1 is calculated at the shift operation, a shaft power device 27 is operated at the plungeable timing, and then, the spline teeth 26b1 of the sleeve 26 can plunge into the clutch groove 23e1 without hitting on clutch teeth 23c1. The spline teeth 26b1 and the clutch teeth 23c1 are engaged with each other, and consequently the sleeve 26 and a clutch ring 23 rotate simultaneously. By this, the shift operation is completed.