In this paper, a dual-band perfect metamaterial absorber based on graphene is proposed in the terahertz region. The metamaterial absorber consists of two sizes of graphene disks and a gold film separated by a dielectric spacer in a unit cell. The numerical results demonstrate that the dual-band perfect absorption can be achieved by the superposition of the specific absorption peaks induced by different disks. The resonance frequency can be tuned via controlling the graphene conductivity and the sizes of the disks. The metamaterial absorber can achieve selectively frequency tunability and it can tune each resonance independently. And the dual-band absorption will not be changed when the small disks move along the diagonal within the range of our research. In addition, owing to the symmetry of the structure, the absorber is insensitive to polarization and can keep a high absorptivity with a wide angle. The flexible and simple design makes it possible for our proposed single-layer graphene absorber to be applied in many metamaterial fields, such as sensing, detecting, and cloaking objects.