Abstract: The product of Fourier series and a finite sum of complex Gaussian functions is used to approximate the window function of a hard-edged aperture, an improved algorithm for the beam propagation through a paraxial ABCD optical system with hard-edged aperture is proposed. The transformation of Gaussian beams is taken as an example, an approximate analytical propagation expression in terms of a sum of elementary functions is derived. Numerical calculation results are given and compared with those by the direct integral of the Collins formula and by using Wen’s method. It is shown that the improved algorithm provides a good trade-off between the computational accuracy and computer time, and is applicable to the far field and near field, whereas there are noticeable discrepancies in the near fi