In　this　research,　we　applied　a　polynomial　hybrid　approach　for　modeling　longitudinal　guided　waves　propagating　in　anisotropic　composites　multi-layered　pipes.　Theoretically,　dispersion　characteristic　equations　in　cylindrical　coordinate　system　were　derived　by　introducing　the　state　vector　form　of　displacement　and　stress　components.　In　virtue　of　the　orthogonality　completeness　and　recursion　properties　of　Legendre　polynomial　series,　the　dispersion　curves　of　longitudinal　guided　waves　for　arbitrary　multi-layered　anisotropic　pipes　can　be　obtained　efficiently　and　accurately.　As　an　alternative　serial　approach,　it　solves　the　wave　propagation　problem　of　complex　anisotropic　cylinders,　and　also　avoids　the　tedious　integral　operations　in　the　traditional　Legendre　polynomial　method.　The　reliability　of　the　numerical　results　of　longitudinal　guided　waves　propagating　in　arbitrary　multi-layered　anisotropic　pipes　was　investigated　based　on　the　state　matrix　and　Legendre　polynomial　hybrid　method.　At　first,　we　calculated　the　multi-layered　pipes　composed　of　isotropic　materials　(steel　and　aluminum)　with　different　diameter-thickness　ratios　and　circumferential　orders,　and　the　results　are　consistent　with　the　ones　from　the　global　matrix　method.　Then,　the　numerical　analysis　for　a　triple-layered　adhesive　pipe　was　implemented.　Finally,　the　composite　multi-layered　pipes　with　at　most　16　layers,　which　are　the　T300/914　in　different　orientations,　were　studied.　Meanwhile,　the　effect　of　the　layer　number,　fiber　angle　and　circumferential　order　on　the　propagation　characteristics　of　longitudinal　guided　waves　were　analyzed.　To　demonstrate　the　generality　of　this　approach,　we　compared　the　dispersion　curves　of　flat　plate　case　with　the　results　from　the　cylindrical　case　using　the　same　physical　properties　by　making　the　geometrical　diameter　to　thickness　ratio　infinity.　Furthermore,　the　displacements　and　stress　distributions　were　also　illustrated　at　given　frequencies.　©　2020　Elsevier　B.V.