Process-induced　initial　gradient　stress　is　inevitable　during　the　fabrication　of　fiber　reinforced　polymer　(FRP)　composites.　In　this　research,　governing　wave　equations　with　variable　coefficients　are　established　for　FRP　plates　under　initial　gradient　stress,　based　on　the　acoustoelastic　theories.　The　Legendre　polynomial　(LP)　method　is　utilized　to　derive　the　solving　algorithm.　The　dispersion　curves　are　obtained　without　layer　slicing,　which　provides　a　more　realistic　analysis　model　for　gradient　stress.　The　accuracy　and　convergence　of　the　proposed　method　are　discussed　through　numerical　examples.　The　influences　of　initial　gradient　stress　on　dispersion　slowness　curves　of　Lamb　and　SH　waves　are　analyzed,　considering　the　parabolic　initial　gradient　stress　distribution,　in　which　it＇s　common　in　the　manufacturing　process　of　FRP　composites.　The　effect　of　initial　gradient　stress　distribution　on　the　phase　velocity　is　investigated　in　detail.　The　influence　of　the　anisotropic　effect　of　FRP　on　guided　wave　propagation　under　initial　gradient　stress　is　discussed.　The　numerical　analysis　shows　that　the　behavior　of　guided　waves　is　influenced　not　only　by　the　initial　gradient　stress　but　also　dominated　by　propagation　direction　in　anisotropic　FRP　composite　plates.　These　results　can　provide　a　useful　reference　for　the　testing　based　on　guided　waves　for　FRP　composite,　especially　when　the　initial　gradient　stress　is　encountered.