In this article, a computational method is proposed for computing the Helmholtz integral equation for acoustic radiation and scattering problems with a three-dimensional body shape. Unlike the previous boundary element method, the integration of acoustic properties is based on the global body surface instead of local elements. The approximation function of body geometry and the weighting function of numerical integration are independently chosen. When the singular kernels of Helmholtz equation are regularized as bounded, discontinuous functions, the order of integration polynomials for acoustic properties can be arbitrarily chosen, therefore, the accuracy and efficiency of computation can be increased.