The tight-binding model is used to investigate band structures of zigzag double-walled carbon nanotubes. The intertube interactions significantly change symmetry of energy bands, energy dispersions, Fermi energy, energy gap, and wave functions. Electronic properties are also affected by the magnetic flux and the Zeeman effect. The main features of band structures are directly reflected in optical absorption spectra, such as the blueshift of absorption frequency, the increase of absorption peaks, and the enhancement of spectral intensity. There are certain important differences between zigzag and armchair double-walled systems.