A speed change control method of an automotive automatic transmission in which a turbine rotational speed is caused to change toward a synchronous rotational speed associated with a desired gear stage by engaging a connection-side clutch while disengaging a release-side clutch, to thereby carry out gear-changing. To reduce a speed change shock, a speed change time is rendered stabilized irrespective of vehicle running state, by carrying out feedback control (Step S76) such that the time-dependent change rate (Ns)' of a rotational speed difference between clutch plates and clutch discs of the connection-side clutch becomes equal to a target slip rotational speed change rate (Ni)'.