A control apparatus executes appropriate speed change control under any operating conditions encountered during an up-shift by change-over, without requiring an increase in control logic. Engagement side hydraulic pressure is swept up as a result of an arithmetic operation in torque phase speed change control. Disengagement side hydraulic pressure is calculated by initial speed change control, dependent on the engagement side hydraulic pressure. The engagement side hydraulic pressure is directly controlled and the disengagement side hydraulic pressure is indirectly controlled, i.e. responsive to the engagement side control. Consequently, the same control scheme can be executed regardless of power-on state or power-off state and regardless of vehicle operating conditions.