Based on the cross-spectral density function and the Rayleigh scattering theory, analytical expressions of the radiation force on Rayleigh dielectric sphere and beam intensity distribution of a focused partially coherent elegant Hermite-Gaussian beam are theoretically derived and corresponding numerical calculations are done. The results denote that when the transverse coherence length degree is large, the focused partially coherent elegant Hermite-Gaussian beam gets a hollow beam profile. Furthermore, the hollow size increases as the beam orders increase. With the decrease of the coherence degree, the focused partially coherent elegant Hermite-Gaussian beam gradually transforms into a Gaussian beam. The light intensity peak decreases as the beam orders increase. Two types of particles with different refractive indexes can be stably trapped in a larger range by changing the degree of spatial coherence and selecting appropriate beam orders, beam waists and focus lengths. The acquired results will have some certain theoretical reference value to optical trapping.