The energy and effective mass of a polaron in a parabolic quantum well are studied theoretically by using LLP-like transformations and a variational approach. Numerical results are presented for the polaron energy and effective mass in the GaAs/Al0.3Ga0.7As parabolic quantum well. The results show that the energy and the effective mass of the polaron both have their maxima in the finite parabolic quantum well but decrease monotonously in the infinite parabolic quantum well with the increasing well width. It is verified that the bulk longitudinal optical phonon mode approximation is an adequate formulation for the electron-phonon coupling in parabolic quantum well structures.