PURPOSE: To provide controllability with a specified shift timing by sensing the start or end of actual shifting from the shift condition value which exhibits the progressing state of the shifting, and thereupon sinking or raising the accumulator back pressure of a frictional engaging element to be made by a back pressure control means.

CONSTITUTION: At the time of shifting-up, a shift solenoid 10 switches a shift valve 12 in conformity to a given shift signal so that the oil pressure in an oil path 24 is drained, wherein it is possible to control drop of the oil pressure in the first clutch by controlling the back pressure of the accumulator 14. The back pressure of the accumulator 14 can be adjusted by a duty solenoid 18 and an accumulator back pressure control valve 16. Then the gear ratio with the shift condition value exhibiting the progressing state of the shifting is calculated, and when judgement is passed that sinking to the specified value is attained, the accumulator back pressure is sunk to zero, and the first clutch is disengaged. At the time of down-shifting, the actual shift end is judged from the change in the gear ratio, and the oil pressure of the first clutch is raised.