Functionally　graded　materials　(FGM)　have　received　extensive　attention　in　recent　years　for　their　excellent　structural　properties.　Ultrasonic　guided　waves　(such　as　Lamb　waves)　propagated　in　FGM　plates　possess　obviously　dispersion　characteristics.　Therefore,　it　is　of　great　value　to　extract　the　relationship　between　the　dispersion　curves　of　ultrasound　guided　waves　and　the　material　properties　in　FGM　plates.　In　this　research,　the　theoretical　process　of　calculating　the　propagation　characteristics　of　Lamb　waves　in　FGM　plates　is　deduced　by　combining　the　FGM　volume　fraction　curve　and　Legendre　polynomial　series　expansion　method.　In　this　proposed　method,　it　avoids　slicing　the　FGM　plate　into　multiple　layers.　A　Mathematica　program　for　numerical　calculations　was　developed,　then　the　Lamb　wave　dispersion　curves　were　solved.　For　comparison,　the　Lamb　wave　dispersion　curves　of　sliced　layer　model　of　a　FGM　plate　is　drawn　in　Disperse　software,　the　results　verify　the　validity　of　the　numerical　calculations.　Meanwhile,　in　PZFlex　software,　the　FGM　plates　was　subjected　to　finite　element　simulation,　also　based　on　the　layered　plates　model.　The　acoustic　characteristics　detection　experiment　(also　known　as　V(f,　z)　measurement)　was　performed　in　the　PZFlex　simulation,　and　the　Lamb　wave　dispersion　curves　were　extracted.　The　influence　of　the　change　of　the　gradient　function　on　Lamb　wave　dispersion　curves　was　discussed.