A terahertz leaky wave modulator based on graphene is designed. By changing the Fermi level of graphene, the resonance response of the metasurface based on metal-insulator-graphene(MIG) structures will be changed significantly, which modulates the properties of the terahertz leaky wave. The simulation results show that with the change of Fermi energy from 10 meV to 60 meV and the thickness of dielectric from 20 μm to 200 μm, the 35 GHz frequency scanning range is finally achieved by optimizing the electro-controlled graphene MIG structure, and the electromagnetic response state is changed from the over-damping state to the under-damping state. Meanwhile, it is found that the phenomenon of electromagnetically induced transparency(EIT) can be induced in the under-damping state, but there is only resonant absorption in the over-damping state. Therefore, the MIG structure with this remarkable feature can be applied to highly sensitive biological detection. The device has the characteristics of simple structure and convenient control. It has a wide application prospect in the detection of biomolecules and material refractive index.