The equilibrium geometries, the electronic structures, the vibration properties and the bond properties of the tier-like structures of Mg2B6, Mg4B10, Mg6B13 and Mg8B16 clusters have been studied by the hybrid density functional B3LYP on the 6-31G* level. The calculated results show that the bond lengths are about 0.225~0.235 nm for Mg-B and 0.154~0.191 nm for B-B; the natural charge of B atoms is about –0.29~–1.10 e by population analysis and about +1.24~+1.45 e for Mg atoms; and the dynamic stabilities of Mg4B10 clusters are higher than that of other clusters.