In executing an ETC cooperative downshift operation based on a driver's intent to decelerate, this system executes an engine output increasing control (e.g. a combination of a throttle opening control and a fuel injection restoring control) for increasing the engine output irrespective of driver's accelerator operation. At the timing a reduction amount in an input shaft rotational speed Nt exceeds a predetermined value K after the ETC cooperative downshift control is started, it is presumed that the hydraulic pressure of a to-be-disengaged clutch is already reduced to a hydraulic pressure level equivalent to a predetermined transmission torque capacity that causes no undesirable acceleration or shock even if the engine output increasing control is started. And, under such assumption, the engine output increasing control is started at this timing. Accordingly, the present invention can accurately set the start timing of the engine output increasing control so as to suppress any undesirable acceleration or shock caused by the engine output increasing control.