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The transmission properties of a substrate integrated waveguide (SIW) based on periodic graphene stacks have been theoretically investigated in the terahertz (THz) region. The effects of the dielectric-graphene-dielectric structure of the stack on the propagation properties are shown to be significant and different from the conventional active SIW based on active components. By varying the graphene chemical potential, the cut-off frequency of the proposed waveguide can be dynamically tuned from 3 to 3.7 THz. Moreover, the tunable waveguide displays low leakage loss and single-mode propagation with −120 dB stop-band attenuation. These primary results are very promising for THz integration devices and SIW-based systems.