Abstract: The window function of circular hard-edge apertures is simulated and optimized by the Laguerre-Gauss truncated series, and applied to study the diffraction of Gaussian beams and 0-order Bessel-Gaussian beams by the hard-edge aperture. The results of the axial and transversal intensity distributions of Gaussian beams and 0-order Bessel-Gaussian beams show that the results by the optimized Laguerre-Gaussian truncated series are in good agreement with those by the Fresnel diffraction integral method if the integration plane is not close to the aperture.