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The propagation behavior of Love waves in a layered structure that includes a functionally graded material (FGM) substrate carrying a piezoelectric thin film is investigated. Analytical solutions are obtained for both constant and gradient dielectric coefficients in the FGM substrate. Numerical results show that the gradient dielectric coefficient decreases phase velocity in any mode, and the electromechanical coupling factor significantly increases in the first- and second- order modes. In some modes, the difference in Love waves' phase velocity between these two types of structure might be more than 1%, resulting in significant differences in frequency of the surface acoustic wave devices.