The surface structure, relaxation, and oxygen adsorbed (2×22)R45° Cu(100) surf ace are studied by ab initio total energy calculation. The calculated atomic str ucture for the Cu(100) (2×22)R45°-O surface is quite close to the experiments except the positions of surface layer Cu atoms. The adsorbed O atoms is lying ap proximately 0.02 nm above the outermost Cu layer and produces a hybridized band and yields some localized surface states around 6.4 eV below EF. The calculated work function for studied oxygen adsorbed surface phase is 4.58 eV, w hich is close to that of clear Cu(100) surface (～4.53 eV). It is concluded that the bonding between adsorbate and substrate copper atoms is approximately limit ed to the first surface layer.