The electro-optic effect in LiNbO3 crystal has been analyzed for light propagating near the optic axis with any polarization direction and for an electric field direction perpendicular to the optic axis. The passive and the electrically induced birefringences and the rotation of polarization direction have been calculated, and the conoscopic interference figures under orthogonal polariscopes for different polarization directions and a field in x-axis of LiNbO3 have been plotted. The extinction areas caused by the rotation of polarization direction change with the polarization direction of light, but the two heads of the induced optical axes do not vary, which are always on the induced principal axis with bigger refractive index. The directions of polariscopes are always extinction, and the ±45° directions with polariscopes always have the maximum intensity. The conoscopic interference figures have been demonstrated experimentally by rotating polariscopes directions, which are accord with the theoretically calculating plots.