We theoretically investigate dynamical control of light slowing within the induced transparent window, e.g., in near-infrared frequencies, in electromagnetically induced transparent (EIT) metamaterials loaded by low-lossy graphene. Coupling with graphene enables distinctive optical responses of the "bright" and "dark" resonators in EIT metamaterials, rendering a switching of the transparent window and a modulation on light dispersion. Optical performance of the transparent window manifests continuous tuning as the graphene doping level changes. We show that the active modulation on optical properties of the transparent window enabled by low-lossy graphene is distinctive either by passively adjusting the interspacing between the building blocks of EIT metamaterials, or active tuning by high-lossy graphene. Furthermore, we report that the group refractive index can be in situ tuned dynamically over a broad range, e.g., ∼2 orders for near-infrared frequencies, together with absorption maintained at a level similar to that of the unloaded structure. Our study offers new possibilities towards chip-scale devices, such as active optical switching, filtering, and data storing.