The electronic states of Au-induced atomic nanowires on Ge(0 0 1) (Au/Ge(0 0 1) NWs) have been studied by angle-resolved photoelectron spectroscopy with linearly polarized light. We have found three electron pockets around the [Formula: see text] line, where the Fermi surfaces are closed in a surface Brillouin zone (SBZ). The results indicate 2D Fermi surfaces of Au/Ge(0 0 1) NWs whereas the atomic structure is 1D. On the basis of the polarization-dependent spectra, the relation between SBZ and the direction of the atomic NW, and the symmetry of the surface state are clarified. These are very useful for further studies on the atomic structure of NWs.