The optical properties of quasiperiodic structures as Fibonacci, Thu-Morse, and Cantor sequences containing graphene-based hyperbolic metamaterial have been investigated using the transfer matrix method and the effective medium theory at THz region. The hyperbolic metamaterial layers were considered as a homogeneous anisotropic medium with their optical axis is tilted with respect to the interface of the layers. It is shown that these structures may have some band gaps in both the hyperbolic and elliptical frequency region. Moreover, the effects of the hyperbolic metamaterial layers optical axis orientation, and the graphen surface conductivity on the transmission and absorption properties are discussed. It is found that the transmission and absorption of all selected structures for both TE and TM polarizations are different. Also, the transmission and absorption for TM polarization depend on both graphene chemical potential and optical axis orientation of the hyperbolic metamaterial layers. However, in the TE polarization case, these optical properties of these structures only depend on graphene chemical potential. These interesting results may be used to design controllable terahertz polarizers or filters.