PURPOSE: To prevent hunting of speed change due to variation of car velocity and throttle opening during running on a bad road by providing a bad road running judging means and a hysteresis region enlarging means for enlarging the hysteresis region of a speed change map in the bad road running condition.

CONSTITUTION: Speed change control is conducted by controlling the operation of speed change control solenoids SL1-SL4 of a hydraulic circuit CK of an automatic transmission AT according to the speed change map on the basis of car velocity obtained from wheel speed signals 30,40 and throttle opening 50. In the speed change map for the bad road shown in the upper drawing, as compared with the speed change map for the bad road shown in the lower drawing, an area sandwiched between the shift up line and the shift down line, the area sandwiched between the lock-up ON line and the lock-up OFF line, that is, the hysteresis area is expanded both in the direction of the car velocity and in the direction of throttle valve opening. As the hysteresis area of the speed change map for the bad road is wide as described above, even if the car velocity and the throttle opening vary during running on a bad road, there is no possibility of causing hunting of speed change due to such variation.