A theoretical study on the optical conductivity in the presence of perpendicular magnetic fields and scattering centers such as charged impurities and optical phonons in graphene is presented. The standard Kubo formula is employed to evaluate the magneto-optical conductivity. The screaning effect of the dielectric environment is included in the calculation of the electron-impurity interation and the self-energy induced by impurity and optic-phonon scattering and the Green′s function for a carrier are calculated self-consistently. In a strong magnetic field, the single impurity scattering is a good approximation. It is found that the charged impurity scattering results in a symmetric Landau level broadening while the combined charged impurity and optical phonon scattering can lead to an asymmetric broadening of density of states (DOS). The peak position and intensity of the magneto-optical conductivity depend strongly on the filling factor and the broadened DOS.