The coupled wave equations of volume holographic grating in photorefractive single-axis crystal in the discretional direction of the optical axis are derived in terms of proper coordinate transformation and Kogelnik's one-dimensional coupled wave theory. The influences of the optic axis on the isotropic and anisotropic diffraction properties of volume grating in LiNbO3 crystal are investigated. It is found that when the geometric parameters of the gratings are given, the diffraction efficiency of the isotropic and anisotropic Bragg diffractions can be maximized by properly choosing the direction of optical axis of LiNbO3 crystal. And the approximately proper direction of the crystal axis is given when the corresponding diffraction efficiency is maximum.All the theoretical results are very useful for the optimum design and wide applications of many volume holographic elements based on volume grating structures.