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We propose and numerically analyze a terahertz tunable plasmonic directional coupler which is composed of a thin metal film with a nanoscale slit, dielectricgrating, a graphene sheet, and adielectric substrate. The slit is employed to generate surface plasmon polaritons (SPPs), and the metal-dielectric grating-graphene-dielectric constructs a Bragg reflector, whose bandgap can be tuned over a wide frequency range by a small change in the Fermi energy level of graphene. As a graphene-based Bragg reflector is formed on one side of the slit, the structure enables SPP waves to be unidirectionally excited on the other side of the slit due to SPP interference, and the SPP waves in the Bragg reflector can be efficiently switched on and off by tuning the graphene'sFermi energy level. By introducing two optimized graphene-based Bragg reflectors into opposite sides of the slit, SPP waves can be guided to different Bragg reflectors at different Fermi energy levels, thus achieving a tunable bidirectional coupler.