A lock-up control apparatus includes a kick-down instruction detector configured to detect a kick-down shift transmission instruction during application of a lock-up clutch. A first lock-up control amount changer is configured to change the lock-up control amount when the kick-down shift transmission instruction is detected. An intermediate gear speed determinator is configured to determine whether the kick-down shift transmission instruction includes an intermediate gear speed shift transmission instruction to an intermediate shift transmission gear speed. A second lock-up control amount changer is configured to change the lock-up control amount when the kick-down shift transmission instruction includes the intermediate gear speed shift transmission instruction. A target gear speed shift transmission instruction detector is configured to detect a target gear speed shift transmission instruction. The third lock-up control amount changer is configured to change the lock-up control amount when the target gear speed shift transmission instruction is detected.