A four-arm Archimedean spiral multi-mode OAM (Orbital Angular Momentum) antenna with bandwidth of 1.34GHz-9.53GHz is presented and analyzed. The bandwidth of traditional OAM antenna is dramatically improved by utilizing the self-complementarity between the arms of Archimede spiral. Comparing to the dual arm helical antenna, the vortex electromagnetic wave phase for the proposed scheme shows better continuity and purity, simultaneously more modes are realized. The reflector is arranged under the ground to make the antenna achieve unidirectional radiation characteristics and reduce backward radiation. The mode for l= 0, l= 1, l= 2 and mixed mode l= 1.2 are realized by controlling phase of the four different feed ports. Finally, the effects about the rotation radius for the Archimede spiral on the patterns with various arm width is investigated and discussed. The results are significant consistency with the design, and concurrently superb vortex characteristics are achieved in different modes.