Structural stabilities and electronic properties of medium sized (ZnSe)n(n = 24, 28, 36, and 48)clusters are investigated in this paper. The starting configurations are generated by handmade construction or cutting from bulk material. Some low-energy structures of other II-IV clusters are also considered. The structure optimizations and energy calculations were performed using DMoL package. The results show that the energies of tubular and cage structures are the lowest when n=24, 28, and 36, and the energy of wurtzite (WZ) bulk material is the lowest when n=48. The tubular and cage structures have relatively large HOMO-LUMO gaps, whereas for the onion-like structures and the WZ bulk materials, their energy gaps are smaller than those of the cage and tube structures.