A lock-up clutch (4) by way of which input/output shafts (1a, 2a) of a torque converter (2) are operatively connected to each other is connected to an electronic type pressure control valve (4). During speed changing in a transmission, a problem of interruption of transmission of torque can be solved by turning off the lock-up clutch (4) at the time point when filling of one of speed changing clutches (21 to 24) to be next brought in an operatively engaged state with hydraulic oil is completed. Hydraulic pressure (P t ) in the torque converter (2) is exerted on the back pressure portion of a piston of the lock-up clutch (4), while hydraulic pressure (P t ) in the torque converter (2) is exerted on the proportional solenoid (42) side of the pressure control valve (40). This makes it possible to reduce the initial hydraulic pressure. During speed changing, the lock-up clutch (4) is not fully released from the engaged state but it maintains its operative state at low pressure, causing shock caused by shifting the lock-up state to be reduced. When hydraulic pressure is gradually increased, an extent of opening of the throttle, weight of the vehicle and the current gear ratio are derived so as to vary a rate of the gradual increase of hydraulic pressure depending on values of these parameters. When the vehicle runs at a normal cruising speed, control is carried out such that hydraulic pressure in the lock-up clutch assumes a value peripheral to output torque from the engine. This enables a running region of the lock-up clutch held in an operatively engaged state to be enlarged substantially.