This paper proposes a graphene gap waveguide structure comprising graphene-covered nanowires and graphene layers. The propagating properties of the fundamental mode and their dependence on the structural and material parameters are studied in detail by the finite element method. Results show that the nanowire radius, gap distance, nanowire permittivity, and chemical potential of graphene have a significant impact on the mode transmission properties. By optimizing parameters, the proposed structure can simultaneously achieve long-range propagation of graphene plasmons and deep subwavelength confinement of the mode field. The application of graphene plasmons for the deep-subwavelength transmission of mid-infrared waves offers a theoretical basis and guidance for the design and high-density integration of photonic devices beyond the diffraction limit.