PURPOSE: To prevent the slip of a driving belt from occurring by installing an engine speed variation detecting means, detecting a sudden change in engine speed, and a tension control pressure booster means heightening the extent of tension control pressure as far as the specified one at a time when the sudden change is detected, respectively.

CONSTITUTION: In a forward traveling state when a lockup clutch 36 of a vehicle is engaged, the second line hydraulic pressure is accurately approximated to an ideal curve, but optimum control of the second line hydraulic pressure is prohibited before time equivalent to the criterion value elapses since engagement of the lockup clutch 36 has started. During an engine speed lowering period as long as the specified period from the engagement of the lockup clutch 36, execution of the second line hydraulic optimum control is checked and the second line hydraulic pressure is heightened up to the fundamental output pressure, so that the slip of a transmission belt 44 attributable to enhancement of transfer torque by rotational inertia in the crankshaft 26 of an engine 10 and the input side rotor of a hydraulic coupling 12 is thus eliminated.