  We present electronic band structure of Ag$_5$Pb$_2$O$_6$ with layered
hexagonal structure containing one-dimensional chains and two-dimensional
Kagom\'{e} layers of silver. A half-filled conduction band shows extremely
simple, single nearly-free-electron-like Fermi surface. The conduction band is
composed of an antibonding state of Pb-$6s$ and O-$2p$ mixing with Ag-4d and
$5s$. Mass enhancement in the state density at the Fermi energy is expected to
be negligibly small by comparing with the specific-heat data. Calculated Fermi
velocity is consistent with small anisotropy observed in transport properties.
Doping effects on the electronic structure are also discussed.
