shift is provided a control apparatus of an automatic transmission (14) of a motor vehicle in which the torque is transmitted from a motor (10) via a device hydraulic coupling. In the automatic transmission comprising a plurality of friction elements hydraulically (C0, C1, C2, C3, B1, B2, B3) is carried out a downshift clutch clutch freewheeling period of the vehicle by releasing one friction elements and by engaging the other friction element. A controller of the shift control apparatus detects a difference between the input and output rotational speeds of the fluid coupling device, and increases the motor speed by an amount controlled on the basis of the difference input and output when performing the downshift clutch clutch freewheeling period vehicle speed, so as to bring the vehicle in a minimum driving state in which the engine speed is slightly greater than the speed of rotation of the hydraulic coupling device.