In this paper, the effect of electron-phonon coupling on the bandwidth of impurity absorption has been considered with a one-dimensional model of crystal lattices. The eigenfunctions of lattice vibrations in the presence of an impurity have been seriously treated by using a field theoretic method. The strength of electron-phonon coupling was obtained in analytical form as a function of the wave number k of the phonon, the range of interaction λ, and the parameter P = r′/r. Here r′ and r are respectively the force constant between an impurity and its neighbours and that between the normal neighbouring atoms. The results show that an impurity which causes the force costant to change has a considerable effect on the electron-phonon coupling. Under certain conditions the contribution of an antisymmetric localized mode in an ionic crystal may be much larger than the total contributions of intra-band modes. Especially, it is possible for the so called "critical scattering" to appear in ion crystals. In that case the contribution of intra-band modes may become very small and contribution comes almost entirely from the localized mode. Conversely, in a nonpolar crystal the contribution of the localized mode is generally negligible. The possible meaning of the above result in the problem of three-dimensional crystals was discussed in the final part of this article.