The combination of graphene and metamaterials is the ideal route to achieve active control of the electromagnetic wave in the terahertz (THz) regime. Here, the tunable plasmon-induced transparency (PIT) metamaterial, integrating metal resonators with tunable graphene, is numerically investigated at THz frequencies. By varying the Fermi energy of graphene, the reconfigurable coupling condition is actively modulated and continuous manipulation of the metamaterial resonance intensity is achieved. In this device structure, monolayer graphene operates as a tunable conductive film which yields actively controlled PIT behavior and the accompanied group delay. This device concept provides theoretical guidance to design compact terahertz modulation devices.