We studied the propagation of an electromagnetic (EM) wave in a piezoelectric superlattice. Because of the piezoelectric effect, a transverse polarization can be induced by a longitudinal wave which couples strongly to the EM wave in some particular frequency regions, resulting in the creation of a new type of polariton that does not exist in ionic crystals. The forbidden band associated with the polariton is not due to the Bragg reflection, but rather to the coupling.