The electronic structures of a single-domain Si(001)2 × 1-Na surface at a saturation coverage have been studied by angle-resolved photoelectron spectroscopy (ARPES) with linearly polarized synchrotron radiation (SR). To determine the dispersion of surface states in detail, the ARPES spectra have been measured along several symmetry axes of the 2 × 1 surface Brillouin zone. The result revealed a new assignment of surface-state dispersions. Symmetry properties of upper surface-state bands are determined using a linearly polarized character of SR. It has been found that the upper two surface states have the same symmetries as the dangling bond of the clean Si(001)2 × 1 dimer surface. The electronic structure of the Si(001)2 × 1-Na surface determined here is very similar to that of the Si(001)2 × 1-K surface [Surf. Sci. 261 (1992) 217] and is consistent with that expected for an alkali double-layer model.