A speed change control system for an automatic transmission for motor vehicles having a planetary gear mechanism and a brake band for altering the transmission ratio. The system is to tighten gradually the brake band. The system comprises a servo-piston, a piston rod secured to the servo-piston and to the brake band, and an accumulator piston axially slidably disposed in the bore of the servo-piston. The servo-piston is biased by a first spring for returning the servo-piston for releasing the brake band, and the accumulator piston is biased by a second spring. Apply side and release side oil chambers are formed on opposite sides of the servo-piston, and an accumulator oil chamber is formed by the accumulator piston in the bore. Pressure oil is applied to the apply side oil chamber, so that the servo-piston moves in a brake band engagement direction against the first spring. After that, the accumulator piston moves a predetermined stroke against the second spring. Thereafter, the accumulator piston engages with the servo-piston, so that both pistons move together for tightening the brake band.