Orbital angular momentum (OAM) beams have attracted great attention owing to their excellent performances in imaging and communication. In this paper, a dual-arm Archimedean spiral antenna (DASA) is proposed to generate multiple OAM states with positive and negative values by feeding at the inner and outer ends, respectively. The topological charge of radiated vortex waves is reconfigurable by tuning the operating frequency. Dual-mode OAM states are generated at different working frequencies (l = ±1 at 3 GHz, l = ±2 at 4 GHz, and l = ±3 at 4.8 GHz). Both the simulation and measurement results demonstrate that OAM beams can be generated effectively by the DASA. In addition, a conical cavity is used to increase the gain of the proposed DASA for more than 5 dBi in comparison to the traditional cylindrical cavity. Furthermore, the qualities of the generated OAM modes by the proposed DASA have been evaluated at different operating frequencies of 3 GHz, 4 GHz, and 4.8 GHz, respectively. The OAM modes purities of l = −1, −2, −3, 1, 2, and 3 are predominate with the proportion of about 81%, 70%, 74%, 78%, 77%, and 75%, respectively. Our results demonstrate that the proposed DASA has great potentials in OAM multiplexing communication systems.