The lattice relaxation of a ZnO single crystal with the (0 0 0 1) polar surface terminated by Zn ions was investigated on the basis of DV-Xa calculations. The chemical bonding states of ZnO were evaluated using cluster medals of [Zn13O13] for the (0 0 0 1) surface and [Zn19O20](2-) for the bulk. From bond overlap populations, it was shown that the covalent bond strength of the surface took a maximal value for the lattice elongation of 0.04 nm, being ascribed to the decrease in the antibonding feature between Zn-3d and O-2p orbitals. The covalent bonding plays an important role in the lattice relaxation of the (0 0 0 1) ZnO surface.