We have studied the Rashba spin-orbital effect on a diluted magnetic semiconductor (DMS) quantum well with parabolic potential in the presence of a magnetic field parallel to the z axis, taking into account the Zeeman coupling and the s-d exchange interaction between the carriers and the magnetic ions. We have obtained an analytical expression for the electron energy spectrum, which depends on the magnetic ion concentration, temperature, and strength of magnetic field. By using the obtained energy spectrum, we calculated the electron effective g*-factor. We have found that effective g*-factor increases when the magnetic field increases; by increasing the strength of spin-orbit interaction, the electron g*-factor decreases and by increasing the temperature, the electron g*-factor increases.