Abstract: The propagation of the Bessel-modulated Gaussian beams with quadratic radial dependence (QBG beams) has been studied,where the passage of QBG beams through a first-order paraxial ABCD optical system has been expressed in a closed-form.As an example,the propagation through a thin lens has been discussed.Numerical calculation examples have been presented to illustrate the propagation properties of QBG beams.