Recent works on the self-interaction correction (SIC) for the incomplete cancellation of the self-energy terms in the Coulomb and exchange potentials under the local-density-functional approximation have removed the long-standing discrepancy between the calculated and observed band gap for large-gap insulator crystals. In this paper the SIC theory is applied to the electronic energy structure of impurity atoms in insulator crystals. The total-energy functional, including the SIC term, is expressed in terms of localized orbitals from which the self-consistent-field (SCF) equations for the one-electron wave functions are derived variationally. The resulting SCF equations contain, aside from the Coulomb and exchange interactions in the conventional local-density-functional approximation, a SIC potential which is state dependent. A general scheme for solving the SCF equations using the method of linear combinations of atomic orbitals is presented, and specific application to the case of LiCl:Cu+ is made. The results of the impurity 3d4s and 3d4p absorption in LiCl:Cu+ are compared with the earlier non-SIC calculation and with experiments. © 1985 The American Physical Society.