In a control device of a vehicle including a first power transmission path transmitting a power through a belt-type continuously variable transmission and a second power transmission path transmitting a power through a reduction gear mechanism in parallel between an input shaft and an output shaft and including a dog clutch in series with the reduction gear mechanism in the second power transmission path, when the dog clutch is in an engagement transition state and a rotational speed change of the output shaft is equal to or greater than a predetermined value, the engagement transition state of the dog clutch is canceled to release the dog clutch.