A lock-up clutch control apparatus for controlling a lock-up clutch (6) provided in a torque converter (5) installed between an engine (3) and a transmission (4), is disclosed. The lock-up clutch control apparatus has a differential pressure generator (7,8) which engages, causes a slip of or disengages the lock-up clutch by adjusting the differential pressure supplied to the lock-up clutch (6); a sensor (11/15) for detecting a rotational speed of the engine; a sensor (16) for detecting an input rotational speed to the transmission; and a controller (1). The controller (1) conducts proportional integration control by using a command signal to the differential pressure generator (7,8), so that an actual slip rotational speed, which is the difference between the engine rotational speed (Np) and input rotational speed (Ni) to the transmission, becomes a target slip rotational speed (Nt). The controller is programmed to conduct integration accumulating the difference (ΔN) between the target slip rotational speed (Nt) and the actual slip rotational speed (SN); to determine whether the accumulated integrated value (I) is equal to or higher than a predetermined integration value (It); and to stop the integration when the accumulated integration value (I) is equal to or higher than the predetermined integration value (It).