Based　on　the　Legendre　orthogonal　polynomial　series　expansion　and　the　partial　wave　theory,　a　Legendre　orthogonal　polynomial　method　(LOPM)　is　proposed　to　calculate　the　reflection　and　transmission　coefficients　of　plane　waves　at　the　liquid/solid　interface　of　a　liquid-loaded　functionally　gradient　material　(FGM)　plate.　The　displacement　solutions　in　FGM　plate　are　fitted　approximately　by　Legendre　orthogonal　polynomial　series.　The　stresses　and　the　governing　differential　equations　of　the　FGM　plate　are　derived.　Based　on　the　boundary　conditions　of　the　liquid/solid　interface　and　the　governing　differential　equations,　the　linearly　independent　equations　are　set　up　to　calculate　the　reflection　and　transmission　coefficients.　Meanwhile,　the　expansion　coefficients　of　the　Legendre　orthogonal　polynomials　are　also　obtained.　The　power　function　establishes　the　gradient　model　of　the　mechanical　parameters　along　the　thickness　direction.　The　angular　spectrums　of　reflection　and　transmission　coefficients　from　LOPM　are　in　well　agreement　with　the　calculation　results　from　the　transfer　matrix　method.　By　analyzing　the　convergence　of　the　reflection　coefficient　spectrum,　the　critical　value　of　the　truncated　order　of　Legendre　orthogonal　polynomials　is　determined.　The　mapping　relationship　between　the　FGM　gradient　models　and　the　reflection　coefficient　angular　spectrum,　also　the　frequency　spectrums　and　the　displacement/stress　distributions　can　be　demonstrated　simultaneously,　which　provides　the　theoretical　fundamentals　of　the　ultrasonic　non-destructive　testing　for　the　mechanical　properties　of　FGM　and　extends　the　application　of　the　LOPM.　©　2021　Elsevier　B.V.