Based on the principle of self-imaging, a 1 × 2 graphene waveguide beam splitter is proposed in this work, which can split the graphene surface plasmons excited by far-infrared light. The multimode interference process in the graphene waveguide is analyzed by guided-mode propagation analysis (MPA), and then the imaging position is calculated. The simulation results show that the incident beam can be obviously divided into two parts by the self-imaging of the graphene surface plasmon. In addition, the influences of the excited light wavelength, Fermi level, dielectric environment on the transmission efficiency are studied, which provide a reference for the research of graphene waveguide related devices.