In a speed change control system of an automatic transmission incorporated with an engine, there are provided a speed change mechanism that is able to establish a forward speed or a reverse by engaging a hydraulically operated friction element upon switching of the transmission from a non-travel range to a travel range; and a control unit that controls the hydraulically operated friction element in such a manner that a hydraulic pressure applied to the friction element is feedback controlled in such a manner that when the engine is under a lower load condition, a rate of speed change of rotation of an input shaft of the transmission has a first target rate. The control unit is configured to set the rate of speed change of the input shaft to a second target rate smaller than the first target rate when, upon switching of the transmission from the non-travel range to the travel range, the engine is under a higher load condition; and configured to control the hydraulic pressure of the friction element in a feedback control manner so that the rate of speed change of the input shaft has the second target rate.