The traditional calculation method of frequency-domain Green function mainly utilizes series or asymptotic expansion to carry out numerical approximation. This method requires very careful divisions of the regions the variables of the integrand. Thus the computing process can be time consuming, which greatly affects the calculation efficiency. Gaussian quadrature is applied to the numerical calculation of the frequency-domain Green function and its partial derivatives. The variation trend of Green function and its partial derivatives along the coordinate plane is analyzed. Comparison of the calculation result with that in existing references is made, which shows that the present method has greatly simplified the computing process, reduced the level of divisions of the regions of variables, improved the computing efficiency and provided higher accuracy.