An　analytical　approach　is　used　to　investigate　the　effects　of　covering　layer　thickness　on　the　propagation　behavior　of　Love　waves　in　functionally　graded　piezoelectric　materials　(FGPMs)　covered　with　a　dielectric　layer.　The　piezoelectric　substrate　is　polarized　in　the　direction　perpendicular　to　the　wave　propagation　plane,　and　its　material　parameters　change　continuously　along　the　thickness　direction.　The　dispersion　equations　for　the　existence　of　Love　waves　with　respect　to　phase　velocity　are　obtained　for　electrically　open　and　shorted　cases,　respectively.　A　detailed　investigation　of　the　effects　of　the　covering　dielectric　layer　thickness　on　dispersion　curve,　phase　velocity,　group　velocity,　and　electromechanical　coupling　factor　is　carried　out.　Numerical　results　show　that　for　a　given　FGPM,　the　covering　dielectric　layer　thickness　affects　significantly　the　fundamental　mode　of　Love　waves　but　has　only　negligible　effects　on　the　high-order　modes.　The　changes　in　phase　velocity,　group　velocity,　and　electromechanical　coupling　factor　due　to　the　change　of　gradient　coefficient　of　FGPMs　could　be　approached　approximately　by　changing　the　thickness　of　the　covering　dielectric　layer,　which　imply　a　potential　factor　for　designing　new-type　surface　wave　devices　with　FGPMs.