A graphene-based ultra-wideband terahertz absorber with polarization independent behavior is proposed and analyzed numerically. The proposed unit-cell structure consists of patterned graphene surface and a graphene ground plane separated by a silicon dioxide (SiO2) layer. The simulated results exhibit that the proposed absorber structure can attain over 90% absorptivity from 0.1 to 20 THz with a fractional bandwidth of 198% while fixing the relaxation time and Fermi energy level of graphene as 0.03 ps and 1 eV, respectively. The structure gives exactly the same absorptivity response for all polarization angles rendering it completely polarization insensitive. It maintains above 80% absorptivity until 50° oblique incidence angle for both TE and TM modes. The shielding effectiveness of the proposed absorber is above 61 dB. The polarization conversion ratio of the structure is 0.12 which confirms that it does not act as a polarization converter. The absorption bandwidth can be dynamically tuned by managing the Fermi energy level and relaxation time of graphene without modifying the structure dimensions. To facilitate structure analysis, an equivalent circuit model based on transmission line theory is introduced, and the reliability of the suggested model is validated using full-wave simulation. The proposed structure is compared with similar graphene based absorbers, and it is revealed that the proposed structure has superior performance suitable for EMI/EMC and stealth applications at terahertz range.