We introduced a tunable terahertz broadband absorber with near-unity absorption based on a graphene metamaterial. A periodic array of star-shaped ring graphene resonators along with a silicon dioxide substrate backed with a ground plane forms the absorbing structure. The absorption rate of the ultimate optimal absorber is more than 90% in the 0.8 to 2.4 terahertz frequency range, which is equivalent to a relative bandwidth of 100% at a central frequency of 1.6 terahertz. It is shown that the proposed structure retains its absorption bandwidth with an absorption level of more than 75% up to a 60-deg elevation angle for different wave polarizations. In addition, by increasing the chemical potential of graphene in the proposed structure from 0.1 to 0.9 eV, the absorption rate of the structure can be tuned from 40% to nearly 100%. The effects of different geometrical parameters of the structure on the absorption rate of the structure are also investigated, and the absorption mechanism of the presented absorber is investigated by interference and impedance matching theories. Finally, the simulation results are compared with calculated analytical ones, where good agreement between the results is observed. The proposed absorber has potential application in terahertz frequencies such as cloaking, modulators, tunable filters, sensors, and imaging systems.