Valence-band structures of the polar ZnO surfaces, i.e., ZnO(0001)-Zn and ZnO(000 (1) over bar)-O, have been investigated by angle-resolved photoelectron spectroscopy utilizing synchrotron radiation. On the (1x1) O-terminated surface, surface-localized states forming dispersing bands with a (1x1) periodicity are identified at the upper portion of the valence-band region. The energetic position of these states and the fact that their photoemission intensities are sensitive to gas adsorption suggest that there is a contribution from the O 2p dangling-bond orbital of the surface O atoms. Comparing the valence-band structure of the (000 (1) over bar)-O surface with that of the (0001)-Zn surface, a deviation of the electronic structure in the near surface region from that in the bulk is found to be larger on (0001)-Zn than on (000 (1) over bar)-O. The role of the step structures, which exist on both polar surfaces but with much higher density on the (0001)-Zn surface, in the modification of the electronic structure is discussed.