It is provided a control device of a vehicle power transmission device including a transmission capable of fixing a rotating member with either of engagement of a one-way clutch or engagement of an engagement device, the transmission having a predetermined shift stage formed on condition that at least the rotating member is fixed, if an input torque to the transmission is changed after the engagement of the engagement device, a torque capacity of the engagement device being temporarily reduced without changing the predetermined shift stage, and if a request for applying a driven torque is made during reduction of the torque capacity of the engagement device, the temporarily reduced torque capacity of the engagement device being recovered, and the driven torque being increased depending on a recovery status of the torque capacity.