We design a graphene-based broadband tunable terahertz metamaterial absorber (MMA). Its structure consists of a surface graphene pattern layer, a medium layer and an underlying metal film. CST simulation results show that the absorption bandwidth for more than 90% absorption rate reaches 2.12 THz, and the range is 3.2-5.32 THz. The absorption bandwidth for more than 99% absorption rate reaches 1.38 THz, and the range is 3.45-4.83 THz, which was not achieved by most of the previous MMA. Multiple reflection interference theory is used to confirm the simulation results. In order to explore the physical mechanism of wideband absorption, we study the surface electric field distribution of the structure. We also find that the absorber has polarization insensitivity and wide-angle incidence characteristics. The absorption frequency of the absorber can be adjusted by changing the chemical potential of graphene. Therefore, the absorber has potential applications in terahertz absorption, filtering and sensing.