1. A controller for an automatic transmission wherein oil pressures acting on a plurality of frictional engaging elements are individually controlled by oil pressure control means to selectively switch the frictional engaging elements between an engagement and a release, resulting in a switching from one shift range to another in a shift mechanism, the controller comprising: engine output increasing control means for performing an engine output increasing control to increase an engine output without depending on a driver's accelerator operation when the shift mechanism is down-shifted on the basis of the driver's intention of deceleration; and output increase start timing control means for setting a start timing of the engine output increasing control at a time point at which the oil pressure of a frictional engaging element controlled for release during the down-shift decreases to a level of not higher than a predetermined transfer torque capacity-equivalent oil pressure by operation of the oil pressure control means.