A graphene/dielectric/graphene sub-wavelength waveguide structure with double branched structure is constructed. The frequency-selection characteristic of branch structure is combined with the electrical tunable characteristic of graphene, and the dynamic modulation of the intensity of incident light from visible light to mid-infrared can be achieved. Surface plasmon polaritons keep the light energy within the nanoscale dielectric slit, which causes the modulator to break the diffraction limit and enhance the interaction between graphene and light. Effects of the chemical potential, branch length and dielectric material of graphene on the output light intensity of the waveguide structure are analyzed by finite element method. Simulation results indicate that, when the incident light wavelength is 1550 nm, the branch length is 315 nm and the chemical potential decreases from 0.80 eV to 0.78 eV, the extinction ratio reaches 6.77 dB. Compared with the conventional modulator, the proposed photoelectric modulator can guarantee the high extinction ratio and modulation efficiency, and it is small in size and the structure is compact and simple, which can meet the requirements of large scale integration applications.