The generating of vortex beams in the terahertz (THz) band attracts significant attention due to their applications in high-speed communication and high-resolution imaging. In this article, a novel reflective metasurface working in the THz band is designed to generate four vortex beams with different topological charges in different directions. The unit cell is designed based on the geometric phase, and it consists of two metallic (gold) layers and one dielectric layer in between. The top layer of the unit cell includes an elliptic patch and a circular ring, and the bottom layer of the unit cell is a metallic ground. The reflection efficiency of the unit cell is very high due to the presence of metallic ground. To break through the limitations of traditional methods, the metasurface is a good choice to generate beams that carry orbital angular momentum (OAM). Using the concept of geometric phase, the reflection phase of reflective circular polarization (CP) electromagnetic waves can be controlled in an ingenious way. Owing to the property of the geometric phase, inverse phase shift can be achieved for left-handed circular polarization and right-handed circular polarization waves. By utilizing this trait of geometric phase, one can decompose a linear polarization wave into two orthogonal circular polarization waves and control their properties respectively. By rotating the top layer of the unit cell, 360-degree phase shift and the phase distribution satisfying the requirement for generating the multi-beam multi-mode vortex beam can be achieved. In order to control the direction and the topological charge of each beam, based on the geometric phase, the theory of reflectarray and the phase composition principle, the phase distribution of the reflective metasurface is calculated to provide the phase compensation to make the vortex beams point to certain directions. It is worthwhile to point out that the method presented in this paper provides a way to generate complex multi-mode vortex beams in the THz band. The simulations and measurements show that the metasurface can generate four vortex beams with topological charges l= ± 1 and ± 2 in different directions in the THz band. These results also indicate that our design has great potential applications in wireless communication and high-resolution imaging.