A　numerical　method　is　presented　for　the　investigation　of　the　propagation　characteristic　of　guided　waves　in　functionally　gradient　material　(FGM)　plates.　Based　on　the　State-vector　formalism　and　Legendre　polynomial　method,　the　typical　non-stratified　computing　of　dispersion　curves　of　FGMs　is　realized,　by　introducing　the　univariate　nonlinear　regression　to　optimize　the　arbitrary　gradient　distribution　of　material　component.　Comparing　with　the　conventional　Matrix　method,　the　proposed　method　avoids　the　exhausting　root-locating　algorithm　of　solving　the　transcendental　equation　by　a　single-variable　scanning　process.　This　method　turns　it　into　an　algebraic　eigenvalue　problem,　which　mainly　depends　on　the　orthogonal　completeness　and　strong　recursive　property　of　Legendre　polynomial　series.　It　provides　a　fast　and　flexible　approach　to　extracting　the　dispersion　curves,　displacement　distribution　and　stress　profile,　simultaneously.　Results　from　chrome-ceramic　FGM　plate　are　compared　with　those　from　the　previous　articles　to　confirm　the　feasibility　and　accuracy　of　the　proposed　method.　Then,　this　approach　is　further　applied　to　iron　based　alumina　FGM.　The　dispersion　curves　with　different　gradient　function　are　calculated　to　illustrate　the　influence　of　the　gradient　variation.　Moreover,　the　influence　of　the　cut-off　order　of　Legendre　orthogonal　polynomials　on　the　convergence　of　dispersion　curves　is　also　revealed　through　numerical　examples.　Utilizing　the　mapping　relationship　between　the　gradient　distribution　and　the　propagation　characteristics,　it　gives　theoretical　support　for　nondestructive　evaluation　and　quantitative　estimation　of　the　structural　characteristics　of　FGM　plates.