An　analytical　study　on　transverse　surface　waves　propagating　in　a　functionally　graded　piezoelectric　substrate　carrying　a　metal　layer　of　finite　thickness　was　carried　out.　Dispersion　relations　for　the　existence　of　the　waves　were　obtained　and　the　effects　of　material　gradient　on　wave　propagation　were　quantified.　Numerical　examples　show　that　the　presence　of　the　material　gradient　affects　significantly　the　fundamental　mode　but　has　only　negligible　effects　on　the　higher　order　modes.　Depending　on　whether　the　surface　wave　velocity　is　smaller　or　greater　than　the　bulk　shear　wave　velocity　in　the　metal　layer,　three　different　types　of　the　dispersion　behavior　are　discussed.