graphene metamaterial is numerically investigated in this paper. For the active manipulation of the PIT device, the single-layer graphene is integrated into the proposed structure consisting of the split-ring-resonator (SRR) and the closed-ring-resonator (CRR). Dynamically adjusting Fermi energy in graphene leads to modulation of the PIT window, allowing for the active control of the group delay. From the simulated electrical field distributions and effective circuit model to analyze, the transmission spectrum modulation can be attributed to the altering in the energy loss of the dark mode resonator through the conduction effect of the graphene layer. Our work offers theoretical references for the development of slow light terahertz devices in the future.