A dual-band Fabry-Perot resonator (FPR) antenna is proposed with hybrid graphene-metal structure. It consists of a bandpass frequency selective surface (FSS), as the partially reflective surface, a grounded dielectric layer, and a rectangular waveguide for feeding. The FPR condition is satisfied at two operating frequencies in the lower and upper stopbands of FSS. When the chemical potential of graphene is 0.6 eV, the 3-dB beamwidth in the E- and H-planes are 16° and 55° at 810 GHz, respectively, both equal to 20° at 890 GHz. The directivity is enhanced significantly. Tunable radiation patterns can be achieved by adjusting the chemical potential.