Based on the Huygens-Fresnel integral and the expansion of the hard aperture function into a finite sum of Gaussian functions,the approximation analytical expression of the high-order Bessel-Gaussian beam passing through a paraxial ABCD optical system with a circular aperture is derived. The propagation properties of the high-order Bessel-Gaussian beam through the circular aperture have been studied.The results show that the diffractive properties relative with the truncation parameter β,the order of Bessel...