Based on the generalized Huygens-Fresnel diffraction integral, the propagation of the Bessel-modulated Gaussian beams with quadratic radial dependence (QBG beams) through a circle-apertured ABCD optical system has been studied.-In our treatment the circle function is expanded into a sum of complex Gaussian functions, thus a closed-form propagation expression of QBG beams has been derived. As an application example, numerical calculations have been performed for the focusing of QBG beams by an apertured lens. The calculatied results have shown the advantage of our method, and are in good agreement with those obtained by the straightforward numerical integration of the generalized diffraction formula.