We study the energy levels of an electron (or hole) polaron in a parabolic quantum well structure, includingthe spatial dependence of the effective mass. We also consider the two-mode behaviour of longitudinal opticalphonon modes of the teary mixed crystals in the structure, in the calculation of the effect of the electron-phonon interaction. We calculate the ground state, the first excited state and the transition energy ofan electron(or hole) in the GaAs/Alx Ga1-xAs parabolic quantum well structure. The numerical results show that theelectron-phonon interaction obviously affects the energy levels of the electron (or hole), which are in agreementwith experimental results.