The generation, propagation and application of vortex beams have been hot research topics in recent years. In this paper we introduce the novel multiple-ring vortex beams, including double-ring vortex beams and triple-ring vortex beams, which are generated by the coaxial superposition of multiple Laguerre-Gaussian vortex beams with different topological charge numbers and different waist parameters, and their intensity distribution is of multiple-ring. We study the generation and distribution characteristics of multiple-ring vortex beams theoretically, obtain the computer generated hologram of multiple-ring vortex beams based on conjugate symmetric extension Fourier computer generated holography, and experimentally generate quality multiple-ring vortex beams using a spatial light modulator. Excellent agreement between theoretical and experimental results is observed. The study indicates that each ring of multiple-ring vortex beams carries different orbital angular momentum, and the spatial distribution is independent. The novel multiple-ring vortex beams provide more controllable parameters and more diverse structure distributions, which enable their applications in the fields of micro-manipulation as optical tweezers or optical spanner. Furthermore, they also have potential applications as available encoding tools in optical communication.