In this paper, a dual-band graphene-based frequency selective surface (GFSS) is investigated and the operating mechanism of this GFSS is analyzed. By adjusting the bias voltage to control the graphene chemical potential between 0eV and 0.5eV, the GFSS can achieve four working states: dual-band passband, high-pass low-impedance, low-pass high-impedance, and band-stop. Based on this GFSS, a hexagonal antenna cover loaded on a broadband omnidirectional monopole antenna is proposed, which can achieve independent 360° six-beam omnidirectional scanning at 1.08THz and 1.58THz dual bands. In addition, while increasing the directionality, the peak gains of the dual bands reach 7.44dBi and 6.67dBi, respectively. This work provides a simple method for realizing multi-band terahertz multi-beam reconfigurable antennas.