This　research　presents　a　numerical　method　to　analyze　the　propagation　characteristics　of　guided　waves　in　multilayered　anisotropic　composite　laminates.　The　dispersion　equations　were　derived　theoretically,　while　the　displacement　and　stress　components　of　each　layer　are　expressed　in　the　form　of　state　vectors,　by　combining　the　state-vector　formalism　and　the　Legendre　polynomials　(SVF-LP).　The　displacement　fields　are　fitted　approximately　by　Legendre　polynomials,　and　the　system　of　linear　equations　are　constructed　by　the　orthogonal　projection.　The　eigenvalue/eigenvector　solution　is　established　to　compute　the　phase　dispersion　curves　instead　of　solving　the　transcendental　dispersion　equations.　This　overcomes　the　problem　of　missing　roots　in　traditional　matrix　method　effectively.　In　order　to　verify　the　robustness　of　the　SVF-LP,　three　cases　of　multi-layered　laminates,　formed　by　isotropic　material,　unidirectional　carbon-fiber　epoxy　prepreg　and　fiber-metal　laminate　(GLARE　3-3/2)　are　investigated,　respectively.　The　influences　of　fiber　angle　change　and　the　stacking　sequence　are　primarily　analyzed,　on　the　dispersion　characteristics　and　the　displacement　and　stress　profiles.　The　matrix　method　is　also　carried　out　to　compare　the　accuracy　of　this　proposed　method,　which　is　done　by　the　commercial　software　Disperse.　Finally,　the　displacement　and　stress　profiles　of　fundamental　modes　of　the　guided　waves　in　an　arbitrary　lay-up　quasi-isotropic　plate　at　a　given　frequency　is　discussed　in　details.