A tunable single-layered broadband metamaterial graphene absorber in the THz range is investigated in this paper. The absorber is made up of the ring and disc of the graphene, a metallic ground plane bottom layer and a polyimide spacer layer. The simulated results show that the relative bandwidth of 90% absorbance is 81.44% from 1.15 to 2.73 THz under the normal incident angle. In addition, the absorber is insensitive to the polarization and has a wide range of the incidence for the TE mode and TM mode. Moreover, the absorbance of the absorber can be flexibly changed from 0 to 1 by controlling the Fermi energy from 0 to 1.0 eV.