Nanoantennas play a fundamental role in the nanotechnology due to their capabilities to confine and enhance the light through converting the localized fields to propagating ones, and vice versa. Here, we theoretically propose a novel nanoantenna with the metal-insulator-graphene configuration where a graphene sheet dynamically controls the characteristics of a metallic dipole antenna in terms of near-field distribution, resonance frequency, bandwidth, radiation pattern, etc. Our results show that by modifying dispersion relation of the graphene sheet attached to the insulator through tuning chemical potentials, we can achieve strong mode couplings between the graphene sheet and the metallic nanoantenna on the top of the insulator. Interestingly, the in-phase and out-of-phase couplings between metallic plasmonics and graphene plasmonics not only split the single resonance frequency of the conventional metallic dipole antenna but also modify the near-field and far-field responses of the metal-graphene nanoantenna. This work is of a great help to design high-performance electrically-tunable nanoantennas applicable both in nano-optics and nano-electronics fields.