This paper reports a novel graphene metasurface exhibiting near-unity absorption over a wide bandwidth of 9.74 THz ranging from 2.06 to 11.80 THz with a fractional bandwidth of 140.86% with respect to the center frequency of 6.93 THz within the terahertz gap of the electromagnetic spectrum. The proposed structure consists of two layers of graphene separated by silicon dioxide (SiO 2). On the top of SiO 2 , a modified fractal-shaped 1 nm thick graphene pattern is deposited while a square-shaped graphene pattern of identical thickness completely covers the backside of the SiO 2 substrate. The absorber was found to be polarization independent under the normal incidence of the approaching electromagnetic wave (EM) toward the top layer of the structure due to its 4-fold structural symmetry. The designed structure offers stable absorption up to 60 incident angle under TE polarization and 40 incident angle under TM polarization. The structure is~λ/55.9 thin and maintains periodicity of~λ/21.7; thereby validating the effective homogeneity condition in the sub-wavelength domain. This graphene-based absorber can find several applications including, sensors, detectors, spatial light modulators, and in spectroscopic detectors, and so forth, in the "Terahertz Gap" for next-generation 5G communication system and beyond.