To investigate the capture characteristics of Rayleigh particles by partially coherent crescent like beam (PCCL). The generalized Huygens Fresnel principle was adopted to derive the expression of the cross spectral density and the force on Rayleigh particles of PCCL beams transmitted through an ABCD optical system. Software simulation and theoretical analysis were conducted on the normalized intensity and force distribution on Rayleigh particles of a focused PCCL beam in the focal plane, and the patterns of the intensity and capture force of the focused PCCL beam changing with the beam parameters and focal length were obtained. The results show that when the beam order n=3, the initial waist width w0=0.1 mm, and the coherence length d0=6 mm, the PCCL beam focused by the lens with a focal length of f=12 mm, both high and low refractive index particles can be captured. Since the PCCL beam presents an off-axis light intensity distribution in the focal plane, and the peak light intensity is not at the coordinate origin, the focused PCCL light intensity and the force of Rayleigh particles can be controlled by adjusting the beam order, initial waist width, coherence length and focal length, so as to realize the flexible capture of Rayleigh particles at different positions by focusing the PCCL beam. The results of this study provide a theoretical basis for the stable capture of particles by focusing PCCL beams.