A multispeed automatic transmission includes first, second and third frictional elements and has first, second and third speed stages. The first frictional element is disengaged, engaged and disengaged when the transmission assumes the first, second and third speed stages respectively. The second speed stage is established by a first speed change, and the third speed stage is established by a second speed change. The second frictional element is engaged, disengaged and disengaged when the transmission assumes the first, second and third speed change states respectively. The third frictional element is disengaged, disengaged and engaged when the transmission assumes the first, second and third speed stages respectively. Upon judgment of need of a speed change from the first speed stage to the third is speed stage, the second speed change is started while carrying out the first speed change, and comparison between a hydraulic pressure command value for the first frictional element at the first speed change and another hydraulic pressure command value for the first frictional element at the second speed change is made to select a smaller one, and the smaller value is practically applied to the first frictional element.