We report a first-principles density-functional calculation of the electronic structure and properties of the recently discovered superconducting β-pyrochlore oxide KOs2O6. We find that the electronic structure near the Fermi energy EF is dominated by strongly hybridized Os 5d and O 2p states. A van Hove singularity very close to Ef leads to a relatively large density of states at EF, and the Fermi surface exhibits strong nesting along several directions. These features could provide the scattering processes leading to the observed anomalous temperature dependence of the resistivity and to the rather large specific-heat mass enhancement we obtain from the calculated density of states and the observed specific-heat coefficient. An estimate of Tc within the framework of the BCS theory of superconductivity taking into account the possible effects of spin fluctuations arising from nesting yields the experimental value.