A control device for a continuously variable transmission with an auxiliary transmission which is mounted to a vehicle, and which includes a variator arranged to continuously vary a transmission gear ratio, and an auxiliary transmission mechanism that is disposed in series with the variator, and that has a first shift stage being a forward shift stage, and a second shift stage being the forward shift stage, and having a transmission gear ratio smaller than a transmission gear ratio of the first shift stage, the control device comprising: a cooperative control means configured to perform a cooperative control to shift the auxiliary transmission mechanism, and to shift the variator in a direction opposite to a shift direction of the auxiliary transmission mechanism when the shift stage of the auxiliary transmission mechanism is varied, and the cooperative control means including an inertia phase time period setting control section configured to set a first inertia phase time period which is a cooperative shift inertia phase time period of an overall transmission, and a second inertia phase time period which is shorter than the first inertia phase time period, characterized in that the cooperative control means being configured to shift the auxiliary transmission mechanism during the first inertia phase time period, and to shift the variator during the second inertia phase time period, when the cooperative control in which an input torque to the continuously variable transmission is equal to or smaller than a predetermined value in the cooperative control is judged, and the cooperative control means being configured to shift the auxiliary transmission mechanism during the first inertia phase time period, and to shift the variator during the first inertia phase time period when the cooperative control in which the input torque to the continuously variable transmission is greater than the predetermined value is judged. a cooperative control means configured to perform a cooperative control to shift the auxiliary transmission mechanism, and to shift the variator in a direction opposite to a shift direction of the auxiliary transmission mechanism when the shift stage of the auxiliary transmission mechanism is varied, and the cooperative control means including an inertia phase time period setting control section configured to set a first inertia phase time period which is a cooperative shift inertia phase time period of an overall transmission, and a second inertia phase time period which is shorter than the first inertia phase time period, characterized in that the cooperative control means being configured to shift the auxiliary transmission mechanism during the first inertia phase time period, and to shift the variator during the second inertia phase time period, when the cooperative control in which an input torque to the continuously variable transmission is equal to or smaller than a predetermined value in the cooperative control is judged, and the cooperative control means being configured to shift the auxiliary transmission mechanism during the first inertia phase time period, and to shift the variator during the first inertia phase time period when the cooperative control in which the input torque to the continuously variable transmission is greater than the predetermined value is judged.