PURPOSE: To abate the occurrence of a torque shock by selecting a torque converter via an intermediate state between both slip and open states at the time of driving state trandition at a fuel-cut area and a fuel supply area.

CONSTITUTION: When a driving state of an engine A shifts to the specified decelerating range, a fuel supply is interrupted by a fuel-cut means B. Therefore a lockup clutch F of a torque converter C is selected from an open state to a slip state. On the other hand, if it gets out of the decelerating range and the fuel supply is resumed, the lockup clutch F is selected to the open state. In this case, when the driving state of the engine A passes through the specified range along a boundary with a fuel supply range during the fuel-cut range, a control means H makes a slip value of the lockup clutch F larger than the other ranges in the fuel-cut range by setting of a slip value setting means G, and it is selected at an intermediate state between both open and slip states. Thus, a torque shock is reducible.