A tunable broadband terahertz absorber based on graphene metamaterial is proposed and numerically demonstrated. The absorber consists of three layers: the upper is the graphene metamaterial layer, the middle is the SiO2 layer, and the bottom is the metallic layer. Simulation results demonstrate that the proposed absorber achieves over 90% absorption in 1.11- 2.61 THz with a relative bandwidth of 80.6% when Fermi level ?c=0.7 eV. The peak absorption rate of the proposed absorber can be tuned from 20.32% to 98.56% by changing the Fermi energy of graphene from 0 eV to 0.7 eV. Additionally, the proposed absorber is insensitive to polarization and has high absorbance to wide incidence angles. Such design may have some potential applications in thermal imaging, thermal detecting, and stealth technique.