This paper proposed a metasurface based on the hybrid graphene-metal which can be switched freely between a quarter wave plate and a half wave plate by adjusting the Fermi level of graphene. Numerical simulation results show that when the Fermi level of graphene is 0 eV, the proposed metasurface can realize the conversion from linearly polarized waves to right-handed circularly polarized waves in the frequency range of 1.465-3.44 THz, with a relative bandwidth of 96.5%, and the absolute bandwidth is 1.975 THz. When the Fermi energy level of graphene is 1 eV, the metasurface becomes a broadband cross-polarization converter, that is, one-half wave plate, which can achieve a polarization conversion rate greater than 80% in the frequency range of 1.173-3.44 THz. The relative bandwidth is 98.7%, and the absolute bandwidth is 2.267 THz. In addition, the proposed broadband switchable metasurface has a strong robustness to the angle of incidence. Therefore, it has a good application prospects in the fields of sensing and imaging.