The electronic structures of SrMoO4 crystals containing F and F+ color centers with the lattice structure optimized are Studied within the framework of the fully relativistic self-consistent Dirac-Slater theory, using a numerically discrete variational (DV-X alpha) method. From the calculation, it is concluded that F and F+ color centers have donor energy level in the forbidden band. The electronic transition energies from the donor level to the bottom of the conduction band are 1.855 eV and 2.161 eV, respectively, which correspond to the 670 nm and 575 nm absorption bands. It is predicted that the 670 nm and 575 nm absorption bands originate from the F and F+ centers in SrMoO4 crystals. (C) 2009 Elsevier B.V. All rights reserved.