Based　on　the　linear　three-dimensional　elastic　theory　and　the　mechanics　theory　of　incremental　deformation,　using　the　Legendre　orthogonal　polynomial　expansion　(LOPE)　method,　the　wave　equations　of　Lamb　wave　propagation　in　the　non-principal　symmetry　axes　direction　of　anisotropic　composite　lamina　was　firstly　derived　when　the　initial　stresses　were　applied　in　the　horizontal　and　vertical　directions.　Subsequently,　the　coupled　equations　of　Lamb　wave　propagation　were　numerically　solved.　In　order　to　verify　the　accuracy　of　the　process,　the　dispersion　curves　of　phase　velocity　in　an　isotropic　aluminum　plate　and　anisotropic　composite　lamina　without　loaded　initial　stresses　were　beforehand　calculated　by　LOPE　method　to　compare　with　those　obtained　from　the　commercial　software　of　DISPERSE　(R)　and　available　data.　Then,　a　series　of　cases　referring　to　unidirectional　fiber　reinforced　composite　lamina　were　further　implemented　to　study　the　effects　of　horizontal　initial　stress　and　vertical　initial　stress　on　the　fundamental　Lamb　wave　modes.　The　results　show　that　the　phase　velocity　of　the　A(0)　mode　is　more　sensitive　to　the　implementation　of　initial　stresses　compared　with　the　S-0　mode　and　SH0　mode.　Finally,　the　effect　of　fiber　orientation　was　illustrated　in　details.　(C)　2020　Elsevier　B.V.　All　rights　reserved.