An analytical approach is taken to investigate shear horizontal surface acoustic wave propagation in viscoelastic/piezoelectric structure, where a viscoelastic material thin layer is bonded to a semi-infinite piezoelectric substrate. The analytical solution of dispersion relations are obtained for electrically open and shorted boundary conditions. The phase velocity, displacement and stresses are calculated and discussed in detail. The effect of the viscous coefficient on the properties of the SH-SAW are figured and presented.