Based on the Thue-Morse aperiodic mathematical sequence, a new kind of diffractive optical elements (DOEs), which is Thue-Morse multi-focal vortex lens, is proposed. Compared with the Fresnel vortex lens, the generated beam by the Thue-Morse vortex lens possesses the optical vortices embedded at the axial foci and the symmetry optical vortices have the equal intensity. The simulations and experiments verify the unique diffraction properties of the Thue-Morse vortex lens, which can generate vortices array and realize the trappings of metal particles and dielectric particles of low refractive index. The Thue-Morse vortex lens can be potentially applied in the research fields of micro and nanophotonics.