The　formula　system　of　the　state-vector　and　Legendre　polynomials　hybrid　method　(SV-LPHM)　was　applied　to　produce　the　dispersion　curves　and　mode　shape　for　the　general　anisotropic　multilayer　composite　cylinders　with　whatever　the　dissimilarities　of　the　layer　material　properties.　According　to　relevant　literature＇s　reports,　traditional　Legendre　polynomial　method　was　only　able　to　deal　with　the　multilayer　system　where　the　material　properties　of　adjacent　layers　are　not　significantly　changed.　To　overcome　the　drawback,　we　introduce　the　state　vector　method　to　reshape　the　wave　equation,　boundary　conditions　and　interface　continuous　conditions　of　the　multilayer　hollow　cylinder　in　a　consistent　manner.　Moreover,　expanding　the　displacement　field　by　the　Legendre　polynomials,　and　then　a　complete　and　concise　state　matrix　form　is　formed　for　dispersion　equation　after　complex　algebraic　transformation.　All　the　matrices　involving　the　mass　and　stiffness　have　been　deduced　analytically　by　the　recurrence　relation　and　orthogonality　of　the　Legendre　polynomial.　The　above-mentioned　operation　overcomes　the　cumbersome　when　applying　traditional　Legendre　polynomial　method　to　dealing　with　the　interface　displacement　and　stress　continuity.　Firstly,　we　outlined　the　derivation　of　the　formalism　of　the　hybrid　method　(SV-LPHM)　for　guided　waves　propagating　in　the　anisotropic　multilayer　hollow　cylinder　with　an　arbitrary　number　of　layers.　And　then　we　demonstrated　the　SV-LPHM　technique　on　the　composite　pipe　of　isotropic　material　and　anisotropic　material,　where　the　key-factors　of　phase　speed,　displacement,　and　stress　distribution　were　assessed　and　elaborated　thoroughly.　The　results　confirm　the　exponential　convergence　of　the　SV-LPHM　compared　with　finite　element　methods.　(C)　2019　Elsevier　Masson　SAS.　All　rights　reserved.