We　presented　a　numerical　method　to　solve　phase　dispersion　curve　in　general　anisotropic　plates.　This　approach　involves　an　exact　solution　to　the　problem　in　the　form　of　the　Legendre　polynomial　of　multiple　integrals,　which　we　substituted　into　the　state-vector　formalism.　In　order　to　improve　the　efficiency　of　the　proposed　method,　we　made　a　special　effort　to　demonstrate　the　analytical　methodology.　Furthermore,　we　analyzed　the　algebraic　symmetries　of　the　matrices　in　the　state-vector　formalism　for　anisotropic　plates.　The　basic　feature　of　the　proposed　method　was　the　expansion　of　field　quantities　by　Legendre　polynomials.　The　Legendre　polynomial　method　avoid　to　solve　the　transcendental　dispersion　equation,　which　can　only　be　solved　numerically.　This　state-vector　formalism　combined　with　Legendre　polynomial　expansion　distinguished　the　adjacent　dispersion　mode　clearly,　even　when　the　modes　were　very　close.　We　then　illustrated　the　theoretical　solutions　of　the　dispersion　curves　by　this　method　for　isotropic　and　anisotropic　plates.　Finally,　we　compared　the　proposed　method　with　the　global　matrix　method　(GMM),　which　shows　excellent　agreement.　(C)　2017　Elsevier　Ltd.　All　rights　reserved.