An elliptical dielectric nanowire waveguide with a nested eccentric hollow cylinder is designed, the inner surface and the outer surface of the waveguide are both coated with graphene. The transmission characteristics of the three lowest order modes supported by the waveguide, i.e. the field distribution, the real part of the effective refractive index, the propagation length, and the quality factor, are obtained by multipole method. The results show that the three lowest order modes of the waveguide can be synthesized by the lowest order modes supported by a single cylinder and an elliptic cylinder coated with graphene. With the increase of the radius of the embedded cylinder, the three evaluation indexes of the waveguide increase slightly. The change of the semi major axis of the ellipse will slightly increase the real part of the effective refractive index, propagation length and quality factor of Mode 0 and Mode 1, while Mode2 will slightly decrease. When $a = {{b}} = 170\;{\rm{nm}}$ , the performance of the circular nested circular waveguide becomes slightly worse than that of the structure in this paper. With the decrease of the semi minor axis of the ellipse, the real part of the effective refractive index, propagation length and quality factor for each of the three modes increase to a certain extent, and have the greatest impact on Mode 1. When ${{b}} = {{a}} = 190\;{\rm{nm}}$ , the transmission performance of the circular nested circular waveguide is not so good as that of the structure in this paper. When the distance between the inner rod and the outer rod on the right side increases, the real part of the effective refractive index for each of the three modes decreases, the propagation length and quality factor of Mode 0 and Mode1 gradually decrease, while the propagation length of Mode 2 increases slightly, and the quality factor is basically unchanged. On the contrary, the mode transmission performance can be significantly improved by increasing the working wavelength and Fermi energy and reducing the dielectric constant of elliptical dielectric nanowires. Compared with the circular dielectric nanowire waveguide nested with an eccentric hollow cylinder coated with graphene, the waveguide designed in this paper can be found to have a good transmission performance. These results are verified by the finite element method. This waveguide can provide a theoretical basis for the design, fabrication and application of nested waveguides of the same type.