Based　on　linearly　three-dimensional　elasticity,　the　wave　motion　equations　for　coupled　Lamb　waves　which　propagate　along　non-principal　directions　of　the　material　are　derived　by　using　a　Legendre　orthogonal　polynomial　approach,　and　the　coupled　equations　of　wave　motion　are　solved　numerically.　For　verifying　its　applicability　and　validity,　the　present　approach　is　applied　to　isotropic　material　and　obtained　results　are　compared　with　existing　results.　Then,　the　phase　dispersion　curves　of　coupled　Lamb　waves　along　different　non-principal　directions　are　calculated,　and　the　effects　of　the　different　propagation　directions　on　fundamental　modes　and　high-order　modes　are　investigated.　Finally,　the　distributions　of　phase　and　group　velocities　of　fundamental　modes　are　shown　respectively,　which　are　useful　for　structural　health　monitoring　of　anisotropic　materials.　Simultaneously,　the　reason　that　S0　mode　is　the　most　sensitive　to　the　change　of　the　propagation　direction　is　illustrated　with　both　displacement　distribution　of　fundamental　modes　and　material＇s　anisotropy　property　being　considered.