A lock-up clutch control device is provided for a vehicle having a torque converter with a lock-up clutch disposed between an engine and a continuously variable transmission such that the occurrence of shocks during lock-up engagement is suppressed. The vehicle lock-up clutch control device is provided with a control unit that controls the lock-up capacity based on an engine torque signal when engaging the lock-up clutch. The control unit uses a predictive engine torque as the engine torque signal for use in the lock-up capacity control. The predictive engine torque is calculated based on an engine torque air response delay and a hydraulic response delay in the lock-up differential pressure and is faster in response than the actual engine torque.