The structural, electronic, and magnetic properties of the stoichiometric (001) surface of double perovskite Sr 2 FeMoO 6 have been studied by using a 10-layer FeMoO 4 and SrO terminated (001)-oriented slab model and the first-principles projector augmented wave potential within the generalized gradient approximation as well as taking into account the on-site Coulomb repulsive (U = 2.0 eV for Fe and 1.0 eV for Mo). An outwards relaxation is observed for several layers near surface, and the accompanying layer rumpling has a decrease tend from surface layer to inner layer. Along Fe-O-Mo-O-Fe or Mo-O-Fe-O-Mo chains, the oxygen atom is closer to the adjacent Mo atom than to the adjacent Fe atom. In FeO 6 or MoO 6 octahedra, the two axial TMÀO bonds are not equal, and especially, the surface dangling bond makes the remaining one axial TMÀO bond slightly shorter than four equally equatorial TMÀO bonds. The half-metallic nature and a complete (100%) , S = 1/2) states with positive and negative magnetic moments respectively and thus antiferromagnetic coupling via oxygen between them. There is no direct interaction between two nearest Fe-Fe or Mo-Mo pairs, whereas the hybridizations between Fe 3d and 4s, O 2s and 2p, as well as Mo 4d, 5s and 5p orbitals are fairly significant.