A　new　method　based　on　Legendre　orthogonal　polynomials　method　(LOPM)　is　proposed　to　calculate　the　acoustic　reflection　and　transmission　coefficients　at　liquid/solid　interfaces.　The　displacement　solutions　of　each　layer　in　a　multilayer　plate　are　fitted　approximately　by　multiple　groups　of　Legendre　orthogonal　polynomials.　The　stress　components　and　the　governing　wave　equations　in　the　plate　are　derived.　Reassembling　the　boundary　conditions　of　liquid/solid　interfaces,　solid/solid　interfaces　and　governing　wave　equations,　the　linear　independent　equations　are　established　to　calculate　the　reflection　and　transmission　coefficients　and　the　expansion　coefficients　of　Legendre　polynomials　in　displacement　solutions.　The　transfer　matrix　method　(TMM)　is　used　to　verify　the　accuracy　of　this　proposed　method.　The　relationship　between　reflection　and　transmission　coefficients　with　oblique　incident　angles　and　frequencies　is　discussed.　The　influence　of　the　polynomial　cut-off　order　on　the　calculation　results　is　analyzed,　and　the　displacement　and　stress　profiles　in　multilayer　plate　are　reconstructed.　The　research　extends　the　applicable　range　of　LOPM,　moreover,　lays　the　foundation　of　non-destructive　testing　and　inversion　of　mechanical　properties　and　bonding　quality　of　the　multilayer　structures　by　acoustic　waves.　(C)　2018　Elsevier　B.V.　All　rights　reserved.