A control device of a continuously variable transmission for a vehicle, comprising: a continuously variable transmission mechanism capable of continuously changing a speed ratio; a sub-transmission mechanism provided in series with the continuously variable transmission mechanism, including a first gear position and a second gear position having a smaller speed ratio than the first gear position as forward gear positions and adapted to switch between the first gear position and the second gear position by selectively engaging or releasing a plurality of frictional engagement elements, characterized by: a transmission control unit configured to switch the gear position of the sub-transmission mechanism to the first gear position after the vehicle is stopped with the gear position of the sub-transmission kept in the second gear position; and a during-stop target torque capacity setting unit configured to set a target torque capacity of an engagement-side frictional engagement element, which needs to be engaged for switching the gear position of the sub-transmission to the first gear position, out of the plurality of frictional engagement elements at a startup torque capacity larger than an input torque input to the sub-transmission mechanism while the vehicle is stopped when the gear position of the sub-transmission mechanism is switched from the second gear position to the first gear position while the vehicle is stopped. a continuously variable transmission mechanism capable of continuously changing a speed ratio; a sub-transmission mechanism provided in series with the continuously variable transmission mechanism, including a first gear position and a second gear position having a smaller speed ratio than the first gear position as forward gear positions and adapted to switch between the first gear position and the second gear position by selectively engaging or releasing a plurality of frictional engagement elements, characterized by: a transmission control unit configured to switch the gear position of the sub-transmission mechanism to the first gear position after the vehicle is stopped with the gear position of the sub-transmission kept in the second gear position; and a during-stop target torque capacity setting unit configured to set a target torque capacity of an engagement-side frictional engagement element, which needs to be engaged for switching the gear position of the sub-transmission to the first gear position, out of the plurality of frictional engagement elements at a startup torque capacity larger than an input torque input to the sub-transmission mechanism while the vehicle is stopped when the gear position of the sub-transmission mechanism is switched from the second gear position to the first gear position while the vehicle is stopped. a transmission control unit configured to switch the gear position of the sub-transmission mechanism to the first gear position after the vehicle is stopped with the gear position of the sub-transmission kept in the second gear position; and a during-stop target torque capacity setting unit configured to set a target torque capacity of an engagement-side frictional engagement element, which needs to be engaged for switching the gear position of the sub-transmission to the first gear position, out of the plurality of frictional engagement elements at a startup torque capacity larger than an input torque input to the sub-transmission mechanism while the vehicle is stopped when the gear position of the sub-transmission mechanism is switched from the second gear position to the first gear position while the vehicle is stopped.