In this paper, both geometrical and electronic properties of rutile TiO2 (110) surfaces have been investigated using First-Principles Density-Functional calculations with CASTEP code, the model of stoichiometric surface is a (2x1) super-cell which has 12 atomic-layer slabs with the bottom 6 held fixed, the bridging-oxygen vacancy surface has been constructed by removing a neutral bridging oxygen atom from this surface. For the stoichiometric surface, the atom relaxations are: Ti6f (+0.2865Å), Ti5f (-0.1039Å), O3f (+0.2433Å) and Ob (+0.0075Å), we find no reconstruction and no surface states in the band gap, the density of states (DOS) is similar to the bulk except the lower conduction band intensity, in accord with recent experiments. Whereas, as a result of bridging-oxygen vacancy, the atom relaxations exchanged and reconstruction occur. The 2 excess electrons left behind removal of one bridge O atom are localized on the Ti-t2g conduction band orbitals, convert some of the Ti4+ ions into Ti3+ ions and result a compensatory shift in the Fermi level. The band gaps we calculated for stoichiometric surface is similar to the bulk, but its increase can be found for Ob vacancy surface.