A specially designed tunable hyperbolic metamaterial (HMM) based on plasmon induced transparency (PIT) of fractal in the near-infrared (NIR) regime was proposed. The HMM-layer constitutes the top metasurface, which is comprised of fractal-like nanospheres of silver (Ag) metal. A bilayer of graphene is sandwiched between the top HMM and bottom silicon (Si) substrate. The permittivity of graphene bilayer was deduced corresponding to different chemical potentials (of graphene). PIT of the proposed structure was obtained in the 3000-4000 nm wavelength band by employing the finite difference time domain simulation under the excitation of a fundamental transverse magnetic (TM) mode. The effects of incidence angle and graphene chemical potential on the transmission characteristics were investigated. Furthermore, the PIT windows could be tuned by altering the radii of Ag nanospheres in the HMM layer and chemical potential of bilayer graphene. Such systems would be useful in varieties of applications, e.g., switching, energy harvesting, sensing in environmental, and/or medical diagnostics, particularly in detecting the existing impurities in human blood and urine.