A lock-up clutch control device which controls a lock-up clutch provided in a torque converter installed between an engine and a transmission, is disclosed. The lock-up clutch control device changes over between a converter state and a lock-up state of the torque converter according to a differential pressure command value (LUprs) relating to a differential pressure supplied to the lock-up clutch. The lock-up clutch control device includes a differential pressure generating device (7,8) which generates the differential pressure supplied to the lock-up clutch; input torque detection means (2,14,15) which detects an input torque (Te) to the torque converter; and a controller (1). The controller (1) is programmed to compute a real differential pressure (P_lu) based on the detected input torque (Te) upon completion of the engagement of the lock-up clutch; compute a learning value (P_learn(Tai)) relating to a differential pressure deviation, based on the difference between the computed real differential pressure (P_lu) and differential pressure command value (P_ref) upon completion of the engagement of the lock-up clutch, and store the learning value (P_learn(Tai)); correct a present differential pressure command value (LUprs_slp) based on the learning value (P_learn(Tai)); and send the corrected differential pressure command value (LUprs) to the differential pressure generating device (7, 8).