Every mode of orbital angular momentum vortex beam is orthogonal to each other, which can solve the problem of spectrum shortage well. In order to solve the problem of narrow bandwidth of orbital angular momentum antenna, an ultra-wideband orbital angular momentum four-arm spiral antenna in terahertz band is designed. The relationship between the continuous phase difference of the feed ports and the generated modes is studied. A graphene double ring structure is used and the antenna performance is improved by adjusting and optimizing the antenna structure size. The experimental results show that the vortex beams with mode number 0, 1, 2 and 3 can be generated by simply adjusting the phase difference, and the gain under different mode number is above 7.5 dBi. At the same time, the absolute bandwidth of the designed antenna reaches to 8.85 THz, and the relative bandwidth at the center frequency of 6 THz can reach to 147% with the S11 is -50 dB. The designed antenna is greatly improved compared with the traditional antenna, and provides a certain significance for the terahertz band mode multiplexing in practical application.