Using the full-potential linearized augmented plane wave method, we studied the electronic structure and magnetic properties of SrFeAsF and Co-doped superconductor SrFe0.875Co0.125AsF. It is found that SrFeAsF exhibits a stripe antiferromagnetic ground state, and in SrFe0.875Co0.125AsF the checkboard antiferromagnetic state become a competitive candidate. The Co-doping drastically suppresses the antiferromagnetic order, increases the density of states near the Femi level and enhances the itineranly of 3d electrons. These results show that the superconductivity is induced by the magnetic fluctuations in SrFe0.875Co0.125AsF.