The optical properties and plasmon resonance coupling of double coaxial gold nanotube arrays are investigated. The results show that the optical transmission is highly tunable by varying the thicknesses of the inner and outer nanotubes, the separation between the inner and outer nanotubes, and the dielectric parameters inside, between, and outside the two nanotubes. The shorter-wavelength transmission bands are very sensitive to the modification of the wall thickness of the outer nanotube, the separation, and the dielectric parameters between the double nanotubes. The dipole and multipolar plasmon modes are excited in our model. However, for small separation and refractive index, the dipole normal mode has a leading function in the transmission properties. Compared with the dipolar modes, the contribution of higher-order modes becomes larger as the parameters increase.