A control apparatus for a lock-up clutch of a vehicle having a hydraulic torque transfer device equipped with the lock-up clutch between a power source and an automatic transmission is provided for controlling a hydraulic pressure of hydraulic oil supplied to the lock-up clutch when the clutch is in a slip region. The control apparatus determines whether an oil temperature of the hydraulic oil is lower than a predetermined temperature, calculates a change in input torque of the lock-up clutch, and determines whether the change in the input torque is larger than a predetermined value. When it is determined that the oil temperature of the hydraulic oil is lower than the predetermined temperature and that the change in the input torque is larger than the predetermined value, the control apparatus changes the hydraulic pressure of the hydraulic oil supplied to the lock-up clutch to a predetermined pressure for a predetermined length of time.