The　adsorption　of　NO　molecule　on　Cu2O(111)　non-polar　surface　has　been　studied　with　periodic　slab　model　by　Perdew-Burke-Ernzerh　approach　of　GGA　within　the　framework　of　density　functional　theory.　Two　molecular　orientations,　N-　and　O-down,　over　different　adsorption　sites,　Cu-CUS,　CuCSA,　O-SUF　and　O-SUB　of　the　Cu2O(111)　surface　have　been　considered.　The　optimized　results　indicate　that　the　N-down　adsorption　models　are　sable　than　the　O-down　ones.　The　adsorption　energy　for　the　N-down　mode　over　Cu-CUS　site　is　113.5　kJ　(.)　mol(-1)　while　the　corresponding　value　for　the　latter　mode　is　39.7　kJ　(.)　mol(-1).　Upon　adsorption　on　the　Cu+　cation,　the　NO　molecules　forms　a　bent　Cu+　-NO　bond,　and　the　tilted　angles　are　different　at　the　two　orientations.　The　N-O　stretching　frequencies　for　both　orientations　are　significantly　red-shifted　upon　coordination.　The　frontier　molecular　orbitals　analysis　indicates　that,　for　N-down　and　O-down　orientation,　the　interaction　between　the　adsorbed　molecule　and　the　substrate　mainly　arises　from　the　anti-bonding　pi　orbital　of　NO　and　the　d　orbital　of　copper　atom.　Moreover　the　relaxation　should　be　considered　because　of　the　effects　of　the　geometry　of　Cu2O(111)　surface　upon　the　adsorption　geometries　and　the　binding　energies　of　O-down　adsorption.