“Threshold A is substituted in a power-on state, “threshold B”, which is lower than “threshold A”, is substituted in a power-off state, and “threshold C”, which is lower than “threshold B” is substituted during a brake operation, as a rapid deceleration determination threshold. The rotational speed of an output shaft of an automatic transmission and the rapid deceleration determination threshold are compared to determine whether a vehicle is rapidly decelerating. The engagement state of a lock-up clutch is controlled based on whether the vehicle is rapidly decelerating.