Transversal electro-optic effect of light propagating in arbitrary direction in LiNbO3 is studied based on the index ellipsoid equation. The characteristics of inductive refractive index of crystal in different directions are investigated. When the electric field is applied along y axis, besides light propagating along the c axis, for the cases of light propagating in the c-y or c-x plane, the inductive refractive index is linearly proportional to the applied electric field and the linear curves are different in different propagation directions. In other cases, the inductive refractive index and the applied electric field have different curves of nonlinear variation in different directions. When the electric field is applied along x axis, the inductive refractive index has the similar characteristics. But the propagating directions holding linear relation are related to the c axis by a 45°rotation. The results will be helpful to the new applications of electro-optic effect of LiNbO3 crystal.