Using a transfer matrix method, we study the property of the interface optical-phonon modes (IOPMs) in a finite semiconductor superlattice (SL) with a structural defect layer in the dielectric continuum approximation. The results show that in such a structure there exist two types of localized IOPMs. They may appear either in the minigap or below and above the bulk bands, and their macroscopic electrostatic potentials are located in the vicinity of the defect layer or surface layer. The evolution of the modes localized in the vicinity of a different interface can clearly be tracked. In some cases, the degeneracy between localized IOPMs may occur, but the conservation of the total number of IOPMs is always kept for every value of the transversal wave number.