A control device for a continuously variable transmission includes a lock-up clutch of a torque converter which is arranged to connect and disconnect a power transmission between a power source and the driving wheel, and a control section configured to output a hydraulic pressure command value. The control section is configured to control a transmission gear ratio of the continuously variable transmission and an engagement state of the lock-up clutch in accordance with a traveling state of a vehicle. The control device includes a learning control section configured to perform a learning control of the engagement state of the lock-up clutch with respect to the hydraulic pressure command value, an oil vibration sensing section configured to sense oil vibration of a line pressure, and a learning control prohibiting section configured to prohibit the learning control when the oil vibration sensing section senses the oil vibration.