Fano resonance modulated effectively by external perturbations can find more flexible and important applications in practice. We theoretically study electrically tunable Fano resonance with asymmetric line shape over an extremely narrow frequency range in the reflection spectra of metamaterials. The metamaterials are composed of a metal nanodisk array on graphene, a dielectric spacer, and a metal substrate. The near-field plasmon hybridization between individual metal nanodisks and the metal substrate results into the excitation of a broad magnetic dipole. There exists a narrow interband transition dependent of Fermi energy E f , which manifests itself as a sharp spectral feature in the effective permittivity ε g of graphene. The coupling of the narrow interband transition to the broad magnetic dipole leads to the appearance of Fano resonance, which can be electrically tuned by applying a bias voltage to graphene to change E f . The Fano resonance will shift obviously and its asymmetric line shape will become more pronounced, when E f is changed for the narrow interband transition to progressively approach the broad magnetic dipole.