The geometric structures, relative stability, electronic structure and their size dependence of scandium monoxide（ScnO, n=1—9） clusters are investigated by using density functional theory （DFT） at the BP86/CEP-121G level （the O atom treated with 6-311G** basis sets）. With the cluster size increasing, the geometries of the lowest energy clusters show that the oxygen atom situated on the surface turn to be embed in the interior. The doped O atom enhances the stability, increases the energy gap between the highest occupied molecular orbital and the lowest unoccupied molecular orbital and changes the trends of stability and electronic properties with the cluster size increasing. Results on even-odd oscillation in cluster stability and electronic properties predicted that the oxide clusters with even number of Sc atoms are more stable than the neighboring clusters with odd number of Sc atoms. The calculated vertical ionization energy values agreed especially well with the experimental values. The trend of electron affinities shows an obvious oscillatorg increasing behavior as the cluster size increasing. The stability and electronic structure of ScnO clusters are also characterized by the maximum hardness principle of chemical reactivity.