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As one of the indispensable instruments in many fields, optical tweezers are extensively utilized in micromanipulation. Vortex beams and diverse structured light fields make multi-trap optical tweezers possible. Here, the radiation forces of Laguerre-Gaussian (LG) composite vortex beams exerting on a Rayleigh dielectric particle are investigated. Our results show that the multi-trap optical tweezers can be produced by the Laguerre-Gaussian composite vortex beams, which can trap the particles with both high and low refractive indices in the focus plane at multiple positions. Moreover, by changing the orbital angular momentum (OAM) quantum numbers and energy ratios of the Laguerre-Gaussian modes participated in the superposition, the quantities of the optical traps and the distances between multiple traps can be conveniently adjusted. Our beams can be generated by several methods, which provides more convenience for the creation of multiple optical traps. The results presented in this work are potential in optical micromanipulation, as well as other applications in biology and chemistry. • The radiation forces of Laguerre-Gaussian composite vortex beams are investigated. • The both high- and low-index particles can be trapped at multiple positions. • The quantities and the distributions of the multiple traps can be adjusted. [ABSTRACT FROM AUTHOR]