In practical applications, the performances of conventional metal-insulator-metal (MIM) waveguide structured optical devices cured during fabrication are not dynamically tunable. In order to address the problem that such devices are not dynamically tunable, based on the excellent optoelectronic properties of graphene materials, graphene nanotubes are induced into the metal-insulator-metal waveguide coupled circular resonant cavity structure, thus designing a dynamically tunable MIM-graphene nanotube hybrid structure refractive index sensor in this work. The finite element method (FEM) is used to numerically study the transmission characteristics, electric field distribution and magnetic field distribution of the system, and the theoretical analysis is performed by multimode interference coupled mode theory (MICMT) to verify its correctness. The results show that after adding graphene nanotube to the MIM waveguide coupled ring resonant cavity structure, a Fano resonance peak appears in this system, which originates from the coherent coupling between the TM₁₀ cavity resonance mode and the graphene plasmonic electrical resonance mode. The sensor can dynamically tune the resonance wavelength and linewidth of Fano resonance in a wide wavelength range by changing the chemical potential of graphene, thus realizing the performance tuning of the refractive index sensor. Hence, the problem that the conventional plasma refractive index sensor is not dynamically tunable issolved. In addition, the influence of the geometrical parameters of the structure on the sensing performance of this system is also studied in detail. The sensor sensitivity increases up to 1250 nm/RIU and the quality factor rises up to 42.4 RIU^–1 at the optimal structural parameters. Compared with the traditional metal-insulator-metal waveguide structure design, this device has many merits such as wide operating band range, easy processing and dynamic tunability, which is a guideline for designing the dynamically tunable high performance nano-photonic integrated devices.