A control device for continuously variable transmission, comprising: operating state detection means (9, 10) for detecting an operating state of a vehicle including a vehicle speed and an accelerator pedal opening; control means for controlling a speed ratio of a continuously variable transmission based on the operating state in a normal mode and a linear mode; acceleration request determination means for determining the presence or absence of an acceleration request of a driver based on the accelerator pedal opening; and speed ratio setting means for setting a speed ratio controlled by the control means at an acceleration start vehicle speed (V 0) when determined the presence of an acceleration request of a driver and switching to the linear mode, and for setting the speed ratio controlled by the control means to be smaller with an increase in the acceleration start vehicle speed (V 0) for equal accelerator pedal opening, wherein, the control means updates the acceleration start vehicle speed (V 0) to a vehicle speed at the time of a determination after determining that the accelerator pedal opening has been increased during acceleration, characterized in that the control means sets a continuously variable transmission input shaft rotation speed based on a transmission characteristic before the update of the acceleration start vehicle speed (V 0) as a lower limit value of the continuously variable transmission input shaft rotation speed after the update if the continuously variable transmission input shaft rotation speed based on a transmission characteristic after the update is lower than the continuously variable transmission input shaft rotation speed based on the transmission characteristic before the update. operating state detection means (9, 10) for detecting an operating state of a vehicle including a vehicle speed and an accelerator pedal opening; control means for controlling a speed ratio of a continuously variable transmission based on the operating state in a normal mode and a linear mode; acceleration request determination means for determining the presence or absence of an acceleration request of a driver based on the accelerator pedal opening; and speed ratio setting means for setting a speed ratio controlled by the control means at an acceleration start vehicle speed (V 0) when determined the presence of an acceleration request of a driver and switching to the linear mode, and for setting the speed ratio controlled by the control means to be smaller with an increase in the acceleration start vehicle speed (V 0) for equal accelerator pedal opening, wherein, the control means updates the acceleration start vehicle speed (V 0) to a vehicle speed at the time of a determination after determining that the accelerator pedal opening has been increased during acceleration, characterized in that the control means sets a continuously variable transmission input shaft rotation speed based on a transmission characteristic before the update of the acceleration start vehicle speed (V 0) as a lower limit value of the continuously variable transmission input shaft rotation speed after the update if the continuously variable transmission input shaft rotation speed based on a transmission characteristic after the update is lower than the continuously variable transmission input shaft rotation speed based on the transmission characteristic before the update.