The electronic structure of single crystals Na0.6CoO2, which are closely related to the superconducting Na0.3CoO2.yH(2)O (T(c) approximately 5 K), is studied by angle-resolved photoelectron spectroscopy. While the measured Fermi surface (FS) is consistent with the large FS enclosing the Gamma point from the band theory, the predicted small FS pockets near the K points are absent. In addition, the band dispersion is found to be highly renormalized, and anisotropic along the two principal axes (Gamma-K, Gamma-M). Our measurements also indicate that an extended flatband is formed slightly above E(F) along Gamma-K.