We propose a novel simple patterned monolayer graphene metamaterial structure based on tunable terahertz plasmon-induced transparency (PIT). Destructive interference in this structure causes pronounced PIT phenomenon, and the PIT response can be dynamically controlled by voltage since the existence of continuous graphene bands in the structural design. The theoretical transmission of this structure is calculated by coupled mode theory (CMT), and the results are highly consistent with the simulation curve. After that, the influence of the graphene mobility on the PIT response and absorption characteristics is researched. It is found that the absorption efficiency of our designed structure can reach up to 50%, meaning the structure is competent to prominent terahertz absorber. Moreover, the slow-light performance of this structure is discussed via analyzing the group refractive index and phase shift. It shows that the structure possesses a broad group refractive index band with ultra-high value, and the value is up to 382. This work will diversify the designs for versatile tunable terahertz devices and micro-nano slow-light devices.