In this study, we demonstrate the tunable modulation of the electromagnetically induced transparency (EIT) effect using L-shaped complementary graphene metamaterials. The structure consists of a horizontal line slot and a vertical line slot, representing the bright and dark modes, respectively. The synergistic interaction between the bright and dark modes generates a pronounced transparent window within the transmission spectrum. Owing to symmetry, the EIF effect can be realized in two perpendicular polarization directions. Compared to metallic metamaterials, graphene metamaterials are tunable by controlling the Fermi energy of graphene via the gate voltage rather than by redesigning the structure. The regulation of the Fermi energy level in the complementary graphene metamaterials presented herein is more straightforward than that in the discrete graphene configurations. By tuning the EIT transparent window, we enabled actively controlled sensing capabilities and the realization of slow light effects. This work illuminates potential applications in the development of environmental sensors, slow-light devices, and terahertz modulators.