In order to explore the trapping properties of a focused twisted Hermite-Gaussian-Schell model beam on Rayleigh particles, based on the generalized Huygens-Fresnel principle and the Rayleigh scatteringtheory, the analytical expressions of light intensity and radiation force of a focused twisted Hermite-Gaussian-Schell model beam passing through a focused lens are derived, and then the effects of beam parameters such as beam order, twist factor and lens focal length on the radiation force of a focused twisted Hermite-Gaussian-Schell model beam are numerically simulated. The results show that the intensity distribution of a focused twisted Hermite-Gaussian-Schell model beam gradually splits and rotates around the transmission axis during the propagation, and the gradient force and trapping stable range of the beam increase with the beam order and twist factor. By selecting appropriate beam parameters and lens focal length, two types of Rayleigh particles with different refractive index can be stably trapped. The results are valuable for the application of focused twisted Hermite-Gaussian-Schell model beams in optical tweezers.