During a shift operation, a time interval TT which is required to switch a mechanical gear ratio is detected. To bring it into coincidence with a reference value, the duty cycle with which a linear solenoid valve SL6 which determines a back pressure on an accumulator is energized is adjusted. The duty cycle is adjusted in accordance with an oil temperature, a throttle valve opening and a shift mode of an automatic transmission in order to prevent the occurrence of shift shocks as a result of a variation in the shift response of the automatic transmission from transmission to transmission or with time.