The invention has been made to eliminate a feeling of two-phase speed-change operations by causing a speed-change operation to proceed continuously when the speed-change operation is performed through two-phase control of engagement and release of four engagement elements. To accomplish this purpose, the invention provides a control apparatus for an automatic transmission wherein a predetermined speed-change operation is achieved through a pre-phase speed-change operation in which a first engagement element and a third engagement element are released and engaged respectively and through a post-phase speed-change operation in which a second engagement element and a fourth engagement element are released and engaged respectively. The control apparatus sets a target rotational acceleration of an input shaft of the transmission, and controls release of the second engagement element for a transition to the post-phase speed-change operation in accordance with the target rotational acceleration. Thus, the input speed during the transition from the pre-phase speed-change operation to the post-phase speed-change operation changes continuously, so that bluntness is prevented from being caused between the pre-stage and post-stage speed-change operations.