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We propose and numerically analyze a mid-infrared electrically controllable plasmonic waveguide directional coupler that is composed of two parallel identical straight dielectric loaded graphene plasmonic waveguide and S-shaped waveguide bends. By varying the Fermi energy level of the graphene sheet, the maximum power coupled from the input waveguide to the cross-waveguide and the corresponding coupling length could be effectively tuned. Under different Fermi energy level, this directional coupler could serve as an electrically controlled optical switch or a 3-dB splitter around the wavelength of 10.5 μm. Moreover, the size of the entire device is really in sub-wavelength scale making it very facilitative for high density integration.