The propagation of shear horizontal (SH) wave in a piezoelectric coupled plate is investigated in this paper. Full account is taken of the piezoelectric coupling effect to the isotropic metal core in the mathematical model. One of the applications of this research is in the damage detection of the host metal structure from the wave propagation signal excited by the piezoelectric layer which is surface bonded on the surface of a metal core. This research is distinct from the previous works on SH propagation in piezoelectric structures because the piezoelectric materials were used as the core structure in the previous studies, and the potential of the studies was mainly on time-delay devices. The dispersive characteristics and the mode shapes of the transverse displacement and the electric potential of the piezoelectric layer are theoretically derived. The results from numerical simulations show that the phase velocity of the plate structure tends to the bulk shear wave velocity of the host metal core at high wavenumber when the shear wave velocity of host plate is larger than that of PZT bonded on it. Furthermore, there are three asymptotic solutions of wave propagation when the shear wave velocity of the host plate is smaller than that of PZT. The mode shape of the electric potential of the piezoelectric layer changes from the quadratic shape at lower wavenumber and with thinner piezoelectric layer to the shape with more zero nodes at higher wavenumber and with thicker piezoelectric layer. These findings are significant in the application of wave propagation in piezoelectric coupled structures.