A control device of a lock-up clutch of a torque converter interposed between a transmission and engine used with a vehicle, is disclosed. The control device has a sensor which detects an input rotation speed to the torque converter, a sensor which detects an output rotation speed from the torque converter, a differential pressure control device which controls the differential pressure applied to the lock-up clutch, and a controller which sets a target slip rotation speed of the torque converter; calculates a real slip rotation speed which is a difference between the detected input rotation speed and the detected output rotation speed; and performs feedback control to determine the differential pressure applied to the lock-up clutch so that the real slip rotation speed coincides with the target slip rotation speed. The controller is programmed to: set the target slip rotation speed to a first target slip rotation speed determined from a vehicle running parameter; perform feedback control so that the real slip rotation speed coincides with the first target slip rotation speed; change over the first target slip rotation speed to a second target slip rotation speed according to an error between the first target slip rotation speed and the real slip rotation speed; after changing over, and perform feedback control so that the real slip rotation speed coincides with the second target slip rotation speed; wherein the first and second target slip rotation speeds are different functions of time.