The dispersion properties of an anisotropic metamaterial composed of periodic stacking of graphene-liquid crystal layers are investigated in the far-infrared region. It is represented that this structure is able to show both the elliptic and hyperbolic dispersions using the tunable properties of the graphene and liquid crystal. The switching between two dispersion phases via control of the temperature, voltage and external electric field is studied. It is shown that this switching can be used to control of the transmission and reflection at the interface of the metamaterial and air.
