Abstract: The Legendre Orthogonal Polynomial Method (LOPM) is proposed to calculate reflection and transmission coefficients of acoustic waves at liquid/solid interfaces.The displacement solutions of orthotropic plate are expanded by the Legendre polynomials.Combining the boundary conditions of liquid/solid interfaces and wave governing equations,the linear independent equations are established to calculate the reflection and transmission coefficients.The polynomials expansion coefficients obtained from these equations are used to derivate the displacement distribution.The reflection and transmission coefficients obtained by LOPM for aluminum plate are consistent with those results by Transfer Matrix Method (TMM).For the case of unidirectional fiber reinforced composite plate,the relationship between reflection/transmission coefficients,oblique incident angle or frequency under different azimuth angles are analyzed.The larger frequency-thickness product range can be compute accurately by improving the truncation of Legendre polynomials.This research widens the applicable range of LOPM,and provides useful guidance for the mechanical properties measurement of materials based on acoustic.