There are three different structures of the α-Al2O3(0001) crystal surface b ecause different atoms are terminated on the outermost layer. Our calculations a re based on the density functional theory in local density approximation, and on ultra-soft pseudopotential methods, with the valence orbital expanded in plane- wave by using three-dimensional periodic boundary conditions in κ-space, first ly, the calculation result is that α-Al2O3(0001) crystal surface structure which the outermost layer is terminated by a single layer of Al atoms is much mo re stable than the other two structures. Secondly, a rhombohedral primitive cell is employed to perform cell optimizations, with ten atoms in the unit cell, and the calculated equilibrium parameters are:a0＝0.48178nm,γ＝120.16, which are in excellent agreement with recent experimental values(a0＝0.47591nm ),with a difference of less than 1.3%. Moreover, our calculations are performed with a su per-cell slab model in vacuum environment, in which the outermost layer is termi nated by single Al atoms. By investigating the four-layer relaxation and Al-O a toms population of the surface, we obtain results that the top single Al layer i s an inward relaxation of 0.0792 nm—0.098nm, that is, the second-layer O atoms are turned into the top layer,and the top O and Al atoms population analysis sho w that the valence electrons are concentrated on the surface oxygen ions with a greater probability,it is obvious that the α-Al2O3(0001) crystal surface ap pears in the O-surface state,which is discussed from the microstructure of α-Al 2O3(0001)crystals in details.