The full-potential linearized augmented plane wave method with the generalized gradient approximation for the exchange and correlation potential (LAPW-GGA) is used to understand the electronic band structure of fluorine-arsenide SrFeAsF as a possible parent material for a new group of oxygen-free FeAs superconductors. The electronic bands, density of states, Fermi surface and atomic charges have been evaluated and discussed for high-temperature tetragonal and low-temperature orthorhombic SrFeAsF phases.