An automatic transmission achieves a desired shift through an initial stage shift in which a first engagement element is released and a third engagement element is engaged, and a final stage shift in which a second engagement element is released and a fourth engagement element is engaged. A control apparatus sets an estimated rotation acceleration for a transmission input shaft in accordance with an input torque and an input torque rotation acceleration speed, and controls the release of the second engagement element for moving to the final stage shift according to the estimated rotation acceleration. As a result, it is possible to prevent a shifting delay and/or degradation that occurs between the initial stage and the latter stage by continuous transmission of the input rotation (engine rotation) change when moving from the initial stage to the later stage.