Abstract: In order to study characteristics of metasurface array of discontinuous phase L-shaped antenna in the 1st and 2nd order modes, by using the theory of scattering field with anomalous transmission, a L-shaped antenna structure was designed. By controlling the geometric parameters of the antenna and selecting the array element group, the coverage phase exceeded 2π. According to different topological charges, the vortex phase plates of the 1st order and the 2nd order were designed to produce different order vortex beams. The simulation results show that the simulation efficiency of the vertical polarization direction of the antenna element is about 55% when the incident wave is polarized vertically. When the phase covered 0~2π and 0~4π, the anomalous transmission angles of the linear array are different, -14.7° and -30° respectively. The results are consistent with the generalized Fresnel theory. This study has the important application value in the research of terahertz vortex beam devices.