A tunable graphene nanostructure metamaterial is designed in order to obtain the Electromagnetically Induced Transparency(EIT) which is analogs to the atomic EIT. By placing the light mode and dark mode closer, a transparency window is shaped due to the strong coupling between them. Meanwhile, the effects of gap size, strip length, coupling location, incident polarization angle and refractive index on the EIT phenomenon are investigated. The results show that the coupling strength becomes weaker as the width of gap increases, and a second window occurs when the dark mode shifts away from the center of the light mode. In addition, changing the Fermi energy of the graphene could bring a different transparency window as well as a tunable group delay. This work may provide applications in the field of photonics, biological sensing and slow light devices.