The possible geometrical and electronic structures of (OsnN)0, ±(n=1—6) clusters are optimized by using the density functional theory (B3LYP) at the LANL2DZ level. For the ground state structures of (OsnN)0,±(n=1—6) clusters, the average binding energies, second finite differences, dissociation energies and energy gaps are analyzed. The calculated results show that there are many different isomerides in (OsnN)0,±(n=1—6) clusters. With the increase of number of atoms, the N atom tend to the peripheral endpoint; the clusters show "odd - even" oscillation and "magic number" effect. The cluster is more stable when the number of atoms is even than odd. It was found that the Os3N+ and Os5N+ clusters are the most stable and n=4 clusters is the least stable, yet the stability of (OsnN)0,±(n=1—6) clusters have increased significantly than pure osmium clusters.