In this paper, a dual-band graphene-based absorber is structured and investigated in a terahertz frequency domain. The designed absorber contains a plus-shaped graphene sheet, as well as four dual concentric graphene-based rings. It is designed according to the SiO2-based substrate. A dual concentric graphene ring provides more than 90% absorption from 2.36-3.24 THz, while a plus-shaped graphene sheet is accountable for absorption from 5.0-5.32 THz. The maximum absorption is found at 2.56, 3.08, and 5.16 THz with 99.81%, 97.34%, and 99.74%, respectively. The variation in the chemical potential of the graphene material offers re-configurability in the dual absorption bands. Due to the four-fold symmetry of the designed structure, the absorptivity value is approximately constant for various polarizations with a wide incident angle (more than 60°). The aforementioned features of the proposed graphene-based absorber make it appropriate in a terahertz frequency regime.