The electronic structure of CdSe, CdTe and SnSe are studied using the first-principle scalar-relativistic LMTO-ASA method in the local-density approximation. In the calculation, extra "empty" spheres are introduced on high-symmetry interstitial sites in zinc-blende crystal structure and NaCl crystal structure, and a correction for the leading non-spherical component of the crystal potential is incorporated. The calculated results are compared with the experiment and other non-self consistent calculation.