The propagation behavior of Love waves in a functionally graded layered piezoelectric structure is investigated in this paper. It involves a thin piezoelectric layer, in which the parameters vary linearly in the thickness direction, bonded perfectly to an elastic substrate. By the WKB method, the phase velocity equations are obtained for both electrical open and short cases on the free surface, respectively. The results show that the circular frequency and cut-off frequency increase as the elastic modulus and dielectric constant vary linearly respectively; meanwhile, the number of vibration modes decreases, and the coupled electromechanical factor increases with the decrease of the dielectric constant. Undoubtedly, this is useful for the design of surface acoustic wave (SAW) devices.