A　numerical　method　to　compute　phase　dispersion　curve　in　unidirectional　laminate　is　described.　The　basic　feature　of　the　proposed　method　is　the　expansion　of　fields　quantities　in　single　layer　on　different　polynomial　bases.　The　Legendre　polynomial　method　avoid　to　solve　the　transcendental　dispersion　equation　of　guided　wave.　Guided　waves　that　have　very　close　propagation　constants　are　calculated　with　great　accuracy.　Numerical　solution　of　dispersion　relation　are　calculated　for　guided　waves　propagation　in　orthotropic　unidirectional　fiber　composites.　The　validation　of　the　polynomial　approach　is　depicted　by　a　comparison　between　the　associated　solution　and　those　obtained　using　Transfer　matrix　method.