We theoretically study the combined effect of Al-concentration, hydrostatic pressure, and temperature on the magneto-optical absorption properties of a semi-parabolic quantum well (SPQW) by investigating the magneto-optical absorption coefficient (MOAC) and the full-width at half-maximum (FWHM). The expression of MOAC is expressed by the second-order golden rule approximation where the electron-longitudinal-optical (LO) phonon interaction is taken into account while the FWHM is obtained from the profile of the curves. The numerical calculations are made for a typical GaAs/GaAlAs quantum well. Our results showed that the Al-concentration, hydrostatic pressure, and temperature affect the magneto-optical absorption properties strongly. Threshold energy and the resonant peaks are non-monotonic functions of the Al-concentration. Moreover, it has been revealed that the magneto-optical absorption properties of SPQW can be controlled by changing these parameters.