Functionally　graded　materials　(FGM)　have　received　extensive　attention　in　recent　years　due　to　their　excellent　mechanical　properties.　In　this　research,　the　theoretical　process　of　calculating　the　propagation　characteristics　of　Lamb　waves　in　FGM　sandwich　plates　is　deduced　by　combining　the　FGM　volume　fraction　curve　and　Legendre　polynomial　series　expansion　method.　In　this　proposed　method,　the　FGM　plate　does　not　have　to　be　sliced　into　multiple　layers.　Numerical　results　are　given　in　detail,　and　the　Lamb　wave　dispersion　curves　are　extracted.　For　comparison,　the　Lamb　wave　dispersion　curve　of　the　sliced　layer　model　for　the　FGM　sandwich　plate　is　obtained　by　the　global　matrix　method.　Meanwhile,　the　FGM　sandwich　plate　was　subjected　to　finite　element　simulation,　also　based　on　the　layered-plate　model.　The　acoustic　characteristics　detection　experiment　was　performed　by　simulation　through　a　defocusing　measurement.　Thus,　the　Lamb　wave　dispersion　curves　were　obtained　by　V(f,　z)　analysis.　Finally,　the　influence　of　the　change　in　the　gradient　function　on　the　Lamb　wave　dispersion　curves　will　be　discussed.