An analytical study on transverse surface waves propagating in a functionally graded material carrying a piezoelectric layer is carried out by Wentzel-Kramers-Brillouin technique. Dispersion relations for the existence of the waves are obtained for material gradient of arbitrary functions and the effects of material gradient on wave propagation are quantified. Numerical examples show the presence of material gradient significantly affects long waves but has only negligible effects on short waves. Depending on whether the surface wave velocity is smaller or greater than the bulk-shear-wave velocity in the piezoelectric layer, two different types of dispersion behavior are discussed.