A kind of surface plasmonic waveguide constructed with double elliptical nano dielectric parallel linescoated with graphene is proposed. The dependence of propagation properties on electromagnetic parameters and structure parameters is studied by using the finite element method.The results show that, when the distance between two ellipses is increased, the real part of the effective refractive index is decreased gradually, and the propagation distance is increased first and then is fallen down, and the mode area is increased gradually. The effective refractive index, the propagation length and the mode area can be adjusted finely by the elliptical semi minor axis. It can achieve better transmission effect by reducing the distance between parallel lines and increasing the length of the semi minor axis of the parallel lines through the optimization calculation. The higher the working frequency is, the smaller the real part of the effective refractive index is, the shorter the propagation distance is, and the larger the mode area is. The higher the temperature is, the larger the real part of the effective refractive index is, the shorter the propagation distance is, and the smaller the mode area is. This work provides a theoretical basis for the design, fabrication and application of the surface plasmon waveguide based on graphene material.