For terahertz communication, a beam reconfigurable reflector array antenna based on graphene material is designed, combining the unique advantages of impedance matching and electrical controllability of graphene material compared with metal in terahertz band and the advantages of high radiation efficiency of reconfigurable reflector array antenna. The graphene patch is embedded in the gap of the antenna phase-shifting unit radiation patch, and the surface resistance value can be changed by adjusting the chemical potential of the graphene patch in the software simulation to realize the purpose of dynamically adjusting the antenna unit compensation phase. The simulation results show that when the center frequency is 3.6976 THz, the phase shifter unit has a phase difference of 180° at 0.1 and 4.0 eV. When the chemical potential of the graphene patch is adjusted within 0.1?4.0 eV, the chemical potential is proportional to the phase of the antenna unit. A 4×4 array antenna is designed, and the simulation results show that the array antenna can achieve beam scanning in the range of (-30°, +30°), and the maximum gain is 20.9 dBi. This paper provides a new idea for the study of terahertz reflector array antenna and the application of graphene materials in reconfigurable communication devices.