In an automatic transmission for a vehicle in which frictional engaging elements are selectively actuated by application of a hydraulic pressure for stopping the rotation of a selected one of rotary elements relative to the others thereby changing over the speed ratio, and the hydraulic pressure is subjected to feedback control so that an actual changing rate of the rotation speed of the rotary element can follow up a predetermined reference rate for attaining an ideal speed shift, an initial hydraulic pressure to be supplied to a specific frictional engaging element in the starting stage of a succeeding speed shift is decided on the basis of the detected value of the hydraulic pressure supplied to the specific frictional engaging element in a preceding speed shift. Thus, even when the capacity of the automatic transmission does not primarily match that of an engine combined therewith, the initial hydraulic pressure supplied to the frictional engaging element can be quickly converged to an appropriate value with high accuracy, and the automatic transmission can be satisfactorily combined with any one of engines having different capacities.