A lock-up clutch control device controls a lock-up clutch provided in a torque converter mounted between an engine and a transmission of a vehicle. The lock-up clutch control device switches between a converter state and a lock-up state by controlling a differential pressure supplied to the lock-up clutch. The lock-up clutch control device has a controller and a differential pressure generator for generating the differential pressure in response to a differential pressure command value. The controller calculates a first differential pressure command value which decreases at a predetermined rate, after the vehicle speed becomes a first predetermined speed; sets the differential pressure command value to a second differential pressure command value, before the vehicle speed becomes a second predetermined speed; and sets the differential pressure command value to a value at which the lock-up clutch is immediately released, when the vehicle speed becomes the second predetermined speed.