The radiation force of focused partially coherent radially polarized doughnut beam acting on a particle (r<λ) in the Rayleigh scattering regime is theoretically studied. Based on the Collins formula, expressions of intensity distribution in the focal region are derived, and the interaction forces between light and the Rayleigh particle are calculated using the Rayleigh scattering theory. Numerical calculations are shown to compare the different radiation forces of a partially coherent radially polarized doughnut beam and a partially coherent linear polarized beam. It is found that the radiation forces in the focal field are obviously different with the different correlation widths, and the particles whose refractive index is lower or higher than the ambient can simultaneously be trapped by use of focused partially coherent radially polarized doughnut beams.