In view of the radiation problem of sound source with complex frequency components, firstly, by using Fourier transform, the governing wave equation of sound source propagation in time domain is transformed into Helmholtz equation in frequency domain. Secondly, with multiple equally spaced frequency points selected as the sampling frequency, the boundary element method is adopted to solve the Helmholtz equation of each characteristic frequency, thus obtaining the sound pressure at different positions under different sampling frequency. Finally, the amplitude and phase of sound pressure in frequency domain are transformed into time domain by an inverse discrete Fourier transform. In the application of the boundary element method, based on the conventional boundary integral equation of Helmholtz equation, the boundary is discretized by discontinuous Lagrange element, with the high order continuity of the test function at the node maintained as well. The calculation examples of acoustic eld analysis in two different structures are designed, thus verifying the correctness and accuracy of the algorithm.