The electronic structures of H,O and OH chemisorbed on Si nano-clusters were calculated with local density functional formalism. Atomic force calculations were used to reach at an optimized chemisorption site for the adsorbates. Different models were used. For all H adsorbed clusters, wider energy gaps are opened up compared with that of bulk Si, and quantum size effect is obviously shown. When a shell of the adsorbed H atoms is replaced by oxygen atoms, oxygen induced tail states appear in the gap. Both occupied and unoccupied states exist, and the gap is reduced from that in all H-terminated cases. For O atoms replaced by OH, the tail states become all occupied, but the gap widths do not differ much. No quantum size effects are observable for both O and OH adsorption.