A high-accuracy boundary element method is presented for solving acoustic problems.This new method is based on the acoustical Burton-Miller boundary integral equation,and including the following contents: adopting continuous acoustical elements which can keep the real boundary geometry,ensuring the integral precision of the production of kernel functions and interpolation functions over each element,obtaining the initial solution based on the original mesh,using the relative value of discontinuity of sound pressure gradient as an indicator to judge the convergence of the initial results and to guide mesh refined,computing again and judging whether another mesh refined needed up to obtaining a convergent result.In this thesis,spherical boundary is taken as an example and four types of spherical elements are constructed.The acoustical scattering benchmark is adopted to verify the discretization error indicator which is used to solve complex multi-sphere scattering problems.