The propagation of partially coherent beams through an apertured paraxial ABCD optical system is an interesting but difficult problem encountered in practice. Although the integration based on the Collins formula can be evaluated numerically using such programs as “Mathematia”, it becomes very cumbersome and time consuming with increasing number of apertures. In this paper, by using the method of expanding the hard-edge aperture function into a finite sum of complex Gaussian functions, the recurrence propagation expression for the propagation of partially coherent beams through a multiple apertured ABCD optical system is derived, which provides a fast algorithm for simulating the propagation of partially coherent beams through hard-aperture optics. Numerical calculation examples are given, which show that the calculation results by using our analytical formula are consistent with those by straightforward integral of the Collins formula in the region not close to the aperture. THe main advantage of this method is the fast computation, so that the computing time can be greatly reduced. In addition, the extension to multi-apertured ABCD system is made, where the partial coherence of beams is taken into account, so that the expression is applicable to the more general case and is suitable to partially coherent multimode lasers.