Vortex beams carry orbital angular momentum (OAM), which can increase channel capacity in communication systems. In 2019, the International Telecommunication Union designated the terahertz band as the sixth generation wireless communication carrier, so it is very meaningful to study the OAM of terahertz waves. In this letter, we demonstrated a reflective metasurface terahertz vortex beam generator with a wide operating bandwidth (1.6 ∼ 2.4 THz), which consists of a gold metasurface array and a gold ground plane separated by a polyimide layer. Under illumination of circularly-polarized waves, the proposed metasurface produces vortex beams with topological charges of l = ±1, l = ±2, and l = ±3 with the mode purity larger than 0.6. Simulation results are in good agreement with the theoretical predictions. Our approach provides a new idea for the design of terahertz vortex wave generators.