The nonlinear optical absorption properties via two-photon process of an asymmetrical semi-parabolic quantum well (ASPQW) has been theoretically investigated. The analytical expression for the magneto-optical absorption coefficient (MOAC) is obtained by relating it to the transition probability for the absorption of photons. Meanwhile, the half width at half maximum (HWHM) of the resonant peaks is gained by the profile method. The numerical results are calculated for typical GaAs and GaAs/GaAlAs quantum wells. The obtained results show that MOAC and HWHM are strongly dependent on confinement frequency, magnetic field and temperature in both one- and two-photon processes. The increasing behavior of HWHM on temperature is generally in good accord with the previous reported ones, both theoretically and experimentally.