A control apparatus includes a shift-pressure learning correction controlling section configured to perform a shift-pressure learning correction in which a physical quantity representing a progress of shift is measured at a time of current downshift, and in which an engagement command pressure for a friction element is corrected at a time of next downshift on the basis of a divergence between the measured physical quantity and a target physical quantity; a shift-torque increase controlling section configured to perform a torque increase control in which a command for temporarily increasing torque of a drive source starts to be outputted when a start estimation timing of torque phase has just come during a transition period given between start and end of the downshift; and a learning convergence judging section configured to judges whether the shift-pressure learning correction has converged, configured to prohibit the torque increase control until it is decided that the shift-pressure learning correction has converged, and configured to permit the torque increase control when it is decided that the shift-pressure learning correction has converged.