Asymmetry effects in optical properties of an infinitely long gold nanotube is studied within the framework of the quasi-static approximation. In this way, incident, scattered and transmitted fields are represented with the appropriate electrostatic potentials in the cylindrical coordinates. The problem is investigated using a boundary-value approach. The expressions for the polarizability and dispersion of surface plasmons of the system are derived and numerical results, in the wavelength region 500 nm to 1000 nm, show that instead of the one well-known resonance peak of the nanotube, one pair of resonance peaks appear, as a result of the coupling between the dipole and quadrupole modes. Then, scattering, absorption and extinction widths of the system are formulated. Also, the effective dielectric function of a composite of aligned symmetry-broken gold nanotubes is presented.