We present the tunable multiple plasmon-induced transparency (PIT) in the terahertz region by using a metamaterial made of two graphene bands and a graphene square ring. As the different modes of multiple PIT effects are independent of each other, the physical mechanism behind multiple PIT effects can be revealed by CMT theory. The PIT window changes significantly with the Fermi energy levels and structural parameters of graphene. The both three resonant frequencies increase linearly with the parameters and the Fermi energy changing, which can exhibit high sensitivities and figure of merit (FOM). Meanwhile, the amplitude modulation system can reach 99.63%, which can achieve excellent photoelectric switching. In addition, the group index can be as high as 2739. Therefore, the graphene-based metamaterial could be widely used in switches, modulators, excellent slow-light functional devices and filters in the terahertz region.