Radially polarized beams, focused by a high numerical aperture (NA) objective, have non-propagating fields along the propagation axis in the focal region, which leads to a higher axial trapping efficiency in comparison with linearly polarized beams. We propose a design for converting a lowest-order radially polarized beam (R-TEM01) to a double-ring radial polarization distribution (DR R-TEM01) through a specially designed polarization rotator. The phases of the two rings of this beam differ by π. Numerical results evaluated by rigorous T-matrix method show that the DR R-TEM01 beam can improve the axial trapping efficiency compared with the R-TEM01 beam, provided that the size of trapped particles is of order of the wavelength of the beam.