Based on the generalized Huygens-Fresnel diffraction integral and the expansion of the hard aperture function into a finite sum of complex Gaussian functions,the approximate analytical expression of hypergeometric beams passing through a paraxial ABCD optical system with a circular aperture is derived.Some numerical simulations and analysis are also performed for the transmission characteristics of a hypergeometric beam through a paraxial ABCD optical system with a circular aperture.The obtained results show that light distribution and diffraction effect of hypergeometric beams are closely related to aperture size,transmission distance and beam parameters etc.Compared with the usual way by using diffraction integral formula directly,this method has higher computational efficiency.