Theoretical analysis and numerical results describing the propagation of SH (shear-horizontal) surface waves on piezoelectric ceramics with a depolarized surface layer are described. SH surface waves propagating in piezoelectric ceramics with a depolarized surface layer are shown to be a mixture of the Bleustein-Gulyaev surface wave, electrical potential, and the Love surface-wave mechanical displacement. Depolarization of the surface layer in piezoelectric ceramics produces strong dispersion and a multimode structure of the SH surface wave. The penetration depth of the SH surface waves propagating on an electrically free surface of a piezoelectric ceramic with a depolarized surface layer can be significantly smaller than that of the Bleustein-Gulyaev surface waves propagating on a free piezoelectric half-space. It is concluded that piezoelectric ceramics with a depolarized surface layer can be used in hybrid piezoelectric semiconductor convolvers of reduced size.