A control device for a vehicle transmission equipped with: a friction engagement mechanism for selectively transmitting torque from an input shaft to a power train, and having a continuously variable transmission mechanism capable of continuously changing the gear ratio and a power train having a fixed gear ratio which are provided in parallel between an input shaft to which torque is transmitted from a drive-power source and an output shaft for outputting torque to the drive wheels; and a meshing-type engagement mechanism which makes the power train capable of selectively transmitting torque between the input shaft and the output shaft, and is arranged in series with the friction-engagement mechanism on the downstream side of the friction engagement mechanism in the direction of transmission of torque heading from the input shaft to the output shaft. The control device for the vehicle transmission is configured in a manner such that when transitioning from a state in which the friction engagement mechanism and the meshing-type engagement mechanism are both open and the power train is not capable of transmitting torque to a state in which the meshing-type engagement mechanism is engaged and the power train is capable of transmitting torque to the output shaft, the torque capacity of the friction engagement mechanism is increased to a torque capacity of a level at which the power train rotates, without delaying the start of the engagement of the meshing-type engagement mechanism.
