Vertically well-aligned ZnO nanorod arrays were synthesized on glass substrates by a two-step chemical bath deposition method. The structural and luminescent properties of as-grown and air annealed samples were investigated. Scanning electron microscopy, x-ray diffraction and Raman spectra demonstrate that ZnO nanorods are well oriented with c-axis perpendicular to the substrates. Photoluminescence spectra show a weak ultraviolet emission and an intense broad visible emission band for as-grown and air annealed samples. These visible emission bands exhibit dependences of post annealing temperatures and excitation energies: (1) as the annealing temperature increases, the visible emission band gradually red-shifts from yellow to orange-red; (2) the optimal excitation energy for yellow and orange-red emission band is near the band-gap energy; (3) green emission band can be excited only by the energies lower than the band-gap energy and this emission becomes weak after high temperature annealing. A depletion region model is presented to explain the origins and red-shift of the visible emission bands. The recombination of a delocalized electron in the interstitial zinc close to the conduction band with a deeply trapped hole in the single negatively charged interstitial oxygen center in the deletion region (in the bulk) is responsible for the yellow (orange-red) emission.