In this paper the electronic structures of the complex ion (MnBr6) 4- are calculated with the spin-polarized MS-Xα method under the actual crystal field of symmetry D3d of the crystal CsMnBr3. The one-electron eigenvalues and elgenfunotions and the spin polarization splittings are given. Energies of some optical transitions and the charge transfer transition are calculated based on the transition state theory. The spinorbit coupling constants are calculated with the Oase-Karplus charge parti Won method, and fine structures of the absorption spectra are disoossed.