Broadband metamaterial-based perfect absorbers (MPAs) have significant potential in many applications. However, the design and fabrication of ultra-broadband terahertz MPAs pose considerable challenges. Most terahertz MPAs reported rely on complex, multilayer, or three-dimensional structures that are difficult to fabricate and hard to meet the miniaturization and integration requirements. In this study, we propose and investigate a novel tunable, ultra-broadband terahertz MPA of atomically thin monolayer graphene and hierarchically structured plasmonic metamaterials. The metamaterial MPA consists of alternating T-shaped gold bars, a dielectric layer, and a graphene layer on the bottom gold layer. These near-perfect absorbers exhibit an exceptional absorption of nearly 90% over an ultra-broad frequency range from 20.8 to 39.7 THz; the bandwidth is as high as 18.9 THz. Furthermore, a quantitative analysis of the impact of geometrical parameters on the absorption spectra is conducted. Additionally, the modulation of the absorption window by tuning the Fermi level of graphene is investigated, and the potential applications are discussed.