The Cassegrain telescope is treated as the combination of a beam expander and an annular aperture.Furthermore,by introducing a hard aperture function into a finite sum of complex Gaussian and based on the extended Huygens-Fresnel principle functions,the approximate analytical expression for the intensity distribution of a Gaussian beam passing through Cassegrain antenna in the turbulent atmosphere is derived.The intensity distribution of the diffracted Gaussian beam in the turbulent atmosphere versus the different values of diameter ratio and the different values of the position parameter are also studied and illustrated with numerical calculations.The results of this work have potential applications in study of the far field distribution measurement of the terminals of atmospheric laser communication.