In order to improve transmission efficiency of an automatic transmission, an engagement brake which does not cause drag is used and the surety of its engagement and release, and quick switching between forward maneuver and backward maneuver, is enabled. The automatic transmission comprises a transmission mechanism to achieve forward maneuver and backward maneuver. A backward motion brake which stops the rotation element to achieve backward maneuver is the engagement brake and an input clutch to transfer power by meshing with the rotation element during both forward maneuver and backward maneuver is a friction clutch. The control apparatus executes the control operation to prepare for speedy re-meshing by holding a supply pressure for the clutch hydraulic servo at a sufficient oil pressure to place the pressure in the stand-by condition at the piston stroke position immediately before the start of clutch engagement during the engagement or releasing of engagement of the engagement brake at the time of D.fwdarw.R or R.fwdarw.D shift.