Using the method of series expansion, interface-phonon vibrational modes are calculated in the dielectric continuum model for the graded quantum well of Ga& Al, As with a Gap 6Alp 4As barrier. The intrasubband and intersubband scattering rates are obtained as functions of quantum-well width. The results reveal that the behavior of interface phonon modes is very di8'erent from that in a square quantum-well structure. It is found that the electron -interface-phonon scattering rates can be changed remarkably in a graded quantum-well structure compared with those in a square quantum-well structure, which is usefu1 for some device applications.