A graphene surface plasmon-based nano-parallel wire waveguide composed of two elliptical cylindrical and one cylindrical dielectric nanowires coated with graphene is designed. Using the finite element method, thetransmission characteristics of the five lowest-order modes supported by the waveguide are analyzed. The results show that these modes supported by the waveguide can be synthesized from the fundamental mode and the first-order mode of the graphene-coatedelliptical cylindrical and cylindrical dielectric nanowires. When the working wavelength or the Fermi energy of graphene changes, the changing trend of the transmission characteristics of these modes remains the same. The transmission characteristics of mode 1 and mode 2 are relatively greatly affected by the semi-major axis of the elliptical cylindrical nanowire, the center distance, and the height of the cylindrical nanowire. The transmission characteristics of Mode 3 are relatively less affected by structural parameters. The transmission characteristics of mode 4 and mode 5 are relatively greatly affected by the semi-major axis of the elliptical cylindrical nanowire, the center distance, and the radius of the cylindrical nanowire. The waveguide designed in this paper adopts an elliptical cylindrical structure and increases adjustable parameters. Its transmission performance is better than that of a waveguide composed of three cylindrical dielectric nanowires coated with graphene. The waveguide designed in this paper has certain application prospects in the field of micro-nano optical device integration and sensors.