PURPOSE: To secure the acceleration performance and prevent the deterioration of fuel consumption by not re-coupling a lock-up clutch when the speed change is performed while the engine torque is in the positive state.

CONSTITUTION: When the speed change is judged to be required, a lock-up clutch 28 is released, and the shift process is performed. If the speed change is judged to be in the power-on state, it is reset. When the speed change is judged not to be required and the power-on shift is judged to be completed, the coupling of the lock-up clutch 28 is judged and performed based on the judgment of the decrease of the throttle opening. When a driver performs the speed change while depressing an accelerator, the lock-up clutch is not coupled until the accelerator is somewhat relaxed, and the driver's request for the power performance is satisfied.