We theoretically study the nonlinear optical absorption phenomenon in a GaAs/GaAlAs parabolic quantum well via investigating the phonon-assisted cyclotron resonance (PACR) effect. We find that the two-photon absorption process (nonlinear) is comparable with the one-photon process (linear), and cannot be neglected in studying PACR effect. The additional peaks in the absorption spectrum due to transitions between Landau levels and electric subband energy accompanied by emission and absorption of LO-phonon are indicated. PACR behavior is strongly affected by the magnetic field, the temperature and the confinement frequency. The present work obtains an usefully resonant condition which is more general than and includes the previous resonant behaviors.