In this paper, a novel graphene-based dual-band perfect electromagnetic absorber operating in the mid-infrared regime has been proposed. The absorber has a periodic structure which its unit cell consists of a sliver substrate and two graphene nanoribbons (GNRs) of equal width separated with a dielectric spacer. Two distinct absorption peaks at 10 and 11.33 µm with absorption of 99.68% and 99.31%, respectively have been achieved due to a lateral displacement of the GNRs. Since graphene surface conductivity is tunable, the absorption performance can be tuned independently for each resonance by adjusting the chemical potential of GNRs. Also, it has been proved that performance of the proposed absorber is independent of the incident angle and its operation is satisfactory when the incident angle varies from normal to ±75°. To simulate and analyze the spectral behavior of the designed absorber, the semi-analytical method of lines (MoL) has been extended. Also, the finite element method (FEM) has been applied in order to validate and confirm the results.