In this paper, we design a polarization-independent and angle-insensitive broadband THz graphene metamaterial absorber based on the surface plasmon-polaritons resonance. Full-wave simulation is conducted, and the results show that the designed metamaterial absorber has an absorption above 99% in the frequency range from 1.23 THz to 1.68 THz, which refers to a very high standard. Furthermore, the absorber has the properties of tunability, and the absorption can be nearly adjusted from 1% to 99% by varying the Fermi energy level of the graphene from 0 eV to 0.7 eV. In the simulation, when the incident angles of TE and TM waves change from 0° to 60°, the average absorption keeps greater than 80%. The proposed absorber shows promising performance, which has potential applications in developing graphene-based terahertz energy harvesting and thermal emission.