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.