Theoretically, the diffraction of Gaussian beam limited by the hard-edged aperture is studied and the diffraction distributions of Gaussian beam limited by the apertures with different calibers in Fresnel and Fraunhofer zones are analyzed in detail, and the evolution relationship of the diffraction of Gaussian beam and the different size of the aperture in the different diffraction regions is obtained. The results show that the diffraction of Gaussian beam limited by the pupil function agrees with the Rayleigh diffraction when the caliber of the hard-edged aperture is small enough. These propagation rules of Gaussian beam limited by the aperture could promote the applications of Gaussian beam in the optical communication and the optical super-resolution.