In this investigation, we study the combined effects of a parabolic potential and a Coulomb impurity on the cyclotron resonance of a three-dimensional bound magnetopolaron, under the condition of strong parabolic potential. We only consider the case of weak electron-LO-phonon coupling and apply Larsen's perturbation method to the calculation of energy levels. The polaron resonances in a low-lying energy level are studied and certain cyclotron effective masses are calculated. We apply our calculations to GaAs.