The vortex beams carrying different topological values are generated based on the high efficiency transmission metasurfaces illuminated by quasi-spherical beams from standard horns. These metasurfaces are able to exhibit a transmission efficiency of over 90% in the bandwidth range of larger than 10% and an over 3-bit phase modulation. Through the theoretical derivation of a phase-compensation formula and the design of metasurfaces, high-order orbital angular momentum (OAM) vortex beams are generated on the high efficiency transmission metasurfaces at 30 GHz. The proposed scheme is verified by the full-wave simulation and the results agree well with the theoretical results.