Abstract: The analytical solution to the Frounhofer diffraction of Gaussian beam by a circular aperture is inferred and is compared with the result from the parallel beam. Due to the results of the numerical computation, the distributing curves of light intensity are drawn in the two instances. After the comparison between of the two curves, a conclusion is drawn that when the circle aperture radius a2ww0 the result of Gaussian beam's Frounhofer diffraction is approximate to parallel beam's Frounhofer diffraction. The difference is produced because of ignoring the terms with high degree which n ≥ 2 in the analytics solution.