The electronic energy band structure and linear optical coefficient of LiNbO3 crystal were calculated by first-principle calculation pseudo-potential plane wave method in CASTEP package, and the nonlinear optical coefficient of LiNbO3 was calculated based on coupled Hatree-Fock (CPHF) model. The calculated refractive indices and second-harmonic-generation (SHG) coefficients matched well with experimental results. The results shows that the 4d orbital of Nb atom and 2p orbital of O atom in LiNbO3 crystal are hybridized, which is the origin of the nonlinear property which can be deduced from the characteristics of electronic density of states on upper part of valence bands and bottom part of conduction bands. The calculated results also indicate that the Li－O bond in the crystal shows typical covalent characteristic.