Piezoelectric acoustic waves propagating on glass film/ZnO film/glass substrate structures are theoretically studied. When the thickness of the overgrowth glass film is thin, there exist only the surface waves similar to the Rayleigh waves propagating on ZnO/glass structures. With increasing the overgrowth thickness, there appear the boundary waves, whose particle displacement and electric potential become large at the ZnO layer. The velocity dispersion (velocity vs. ZnO thickness) curve changes very much with increasing the glass thickness, and there appear both dispersive and non-dispersive regions, which correspond to the boundary and surface waves, respectively.