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The focusing properties of radially polarized Bessel-modulated Gaussian (QBG) beam are theoretically investigated in detail by vector diffraction theory. The QBG beam contains an optical vortex. Calculation results show that the intensity distribution in focal region of radially polarized QBG beam can be altered considerably by changing beam parameter and the topological charge of the optical vortex. Beam parameter can induce remarkable focus evolution in axial direction. While topological charge adjusts intensity distribution more significantly in transverse direction, for instance, one focal spot changes into one ring pattern. And some novel focal patterns may occur, including two-peak focus, one ring focus, two-ring focus, three-ring focus, and even dark hollow focus, which is very important in optical tweezers technique.