Based on the far-field Fresnel Kirchhoff diffraction formula and combined with the properties of Bessel function and other special functions,the diffraction intensity distribution of a circular aperture with normal incidence Gaussian beam is calculated. The intensity distribution near the focus is expressed in the form of Lommel function. Then three special regions,namely geometric focal plane,optical axis and geometric shadow region boundary,are selected,and the analytical expression and numerical results of light intensity distribution are given theoretically and numerically. It is found that the smaller the waist radius of Gaussian beam,the larger the radius of the Airy spot,and the greater the focal depth.Finally,the integral intensity of light intensity on the focal plane is calculated. The result indicates that the smaller the waist radius is,the more concentrated the light intensity is to the center. Compared with the diffraction of plane wave,the Gaussian beam will not change the overall contour of the light intensity distribution,but will make the light intensity concentrate to the focus.