Abstract: A control device includes a deceleration flex-torque calculation unit that calculates a target torque capacity of a lock-up clutch when a state of the lock-up clutch is controlled to a deceleration flex control state, an acceleration flex-torque calculation unit that calculates a target torque capacity of the lock-up clutch when the state of the lock-up clutch is controlled to an acceleration flex control state, and a control unit that controls a torque capacity of the lock-up clutch to a target torque capacity calculated by the acceleration flex-torque calculation unit, during a period until a target torque capacity calculated by the acceleration flex-torque calculation unit falls below a target torque capacity calculated by the deceleration flex-torque calculation unit, when the state of the lock-up clutch is shifted from the acceleration flex control state to the deceleration flex control state.