In order to overcome the limitations exhibited by traditional absorbers in electromagnetic wave absorption, such as the extremely narrow absorption bandwidth and uncontrollable absorption results, this paper proposes a novel tunable broadband metamaterial absorber based on graphene. Compared to other terahertz absorbers, the absorber designed in this study exhibits simpler structural design, compact form, thin thickness, efficient absorption performance, and a broader bandwidth. This absorber adopts a three-layer structure, including a patterned monolayer graphene metasurface, a dielectric layer, and a metal substrate. The structure of this patterned graphene consists of four triangular graphene resonators, achieving both high absorption efficiency and maintaining an exceptionally wide absorption bandwidth. The simulation results indicate that at a Fermi energy level Ef of 0.45 eV, the absorber achieves a broadband absorption rate of over 90 % in the 3.287 THz to 5.247 THz frequency range under normal terahertz wave incidence conditions. By analyzing different quantities of the triangular graphene structure on the top of the absorber, we found that the wide absorption bandwidth of the absorber is mainly attributed to the structural coupling of the top-layer graphene in the absorber. Furthermore, through the study of electric field amplitude and current distribution, we stumbled upon that when terahertz waves are incident on the absorber, due to the structural coupling between the graphene layers, electric resonance and magnetic resonance occur within the absorber, resulting in the absorption effect. Finally, through the study of geometric parameters, different polarization angles and oblique incidence angles of the incident waves, as well as different Fermi energy levels of graphene, we discovered that by adjusting the Fermi energy level of graphene, the bandwidth and absorption performance of the absorber can be flexibly tuned. In addition, this absorber exhibits wide-angle absorption characteristics and polarization-insensitive properties, providing potential application prospects in fields such as terahertz thermal imaging and stealth technology.