A metamaterial- and graphene-based broadband terahertz (THz) electromagnetic wave absorber that is composed of a stack of patterned gold film layer, patterned graphene layer, polyimide layer, and silicon layers was studied in detail. Our study is based on numerical simulations and electromagnetic absorption level higher than 90% over 2.09 THz band was demonstrated. The absorption frequency band significantly depends on the thickness of the polyimide layer and red shifts in parallel with its thickness. The major role of the added patterned graphene layer is to introduce frequency tunability property to the almost perfect absorption. As the Fermi level of graphene changed from 0 to 0.6 eV, the center frequency of the absorption band blueshifts from 6.19 to 8.15 THz. We also investigated incoming beam angle of incidence dependence and polarization sensitivity of the absorption. Metamaterial-based tunable absorbers prospected to be utilized in high-performance THz devices as a performance boosting critical element.