In this paper, a graphene-coated hybrid dielectric nano-parallel wire waveguide is designed. This waveguide consists of two cylindrical and one elliptical cylindrical dielectric nano-parallel wires. The five lowest-order modes are classified, the effects of working wavelength, Fermi energy of graphene, and structural parameters on the real part of effective refractive index, propagation length, and quality factor of the five lowest-order modes are investigated by the finite element method. The results show that the five lowest-order modes can be synthesized from the low-order modes of cylindrical nanowires and elliptical cylindrical nanowires. The transmission characteristics of the five modes can be effectively adjusted when the operating wavelength and Fermi energy of the graphene are adjusted. When the structural parameters are changed, the transmission characteristics of the first two modes change significantly, while the transmission characteristics of the other three modes do not change significantly. Compared with a waveguide composed of two elliptical cylinders and a cylindrical dielectric nano-parallel wire, the waveguide structure designed in this paper has a longer propagation length and a higher figure of merit. The theoretical research in this work is helpful to the design, fabrication, and application of graphene coated hybrid dielectric nano-parallel wire waveguides.