We worked out the dielectric constants of x0 and x of the alkali-halide crystal on the basis of the quantum theory of solids. We have used the variational method of Slater and Kirkwood in our energy-calculations and adopted Landshoff's method for evaluating the exchange integrals among the non-orthogonal wave functions. The relation among the various theories, due to Shockley, Mott and Fröhlich, of the dielectric constant of ionic crystal have been clarified from the viewpoint of out theory. The numerical results for LiF are in good accordance with the experiment.