A theoretical treatment was developed to explain the light diffraction bands normal to the c-axis subtending large angle and strong in intensity which were investigated in much details with a -LiIO3 single crystals under the action of a d. c. field. It is assumed only that a fluctuation of the space charge density Sp (x, y) appears as ionic transportation taking place in the c-direction. The related internal field sE (x, y) produces δεij (x, y) for the dielectric tensor through the linear electro-optic effect. As a consequence, anisotropic phase gratings come into existence in the crystal. With such a model we successfully explained quantitatively or qualitatively all observed phenomena such as the polarization of diffracted beams turning π/2, the angular distribution of diffracted intensity being asymmetric and possessing a minimum, and those observed using specimens of different absolute configurations being related as mirror images. The relative positions of the diffracted bands and their shapes observed with specimens cut in different orientations with respect to the c-axis were found in agreement with our theoretical derivation. The variation of the angular position of the minimum intensity with the change of the incident angle were calculated and satisfactory results were obtained. Therewith we evaluated for the first time the ratio of two elements of the electro-optic tensor γ42/γ41=1.6 in a d. c. field.