  We have investigated magnetic and transport properties of the {\it
kagom\'{e}-bilayer} ferromagnet Fe$_{3}$Sn$_{2}$. A soft ferromagnetism and a
large anomalous Hall effect are observed. The saturated Hall resistivity of
Fe$_{3}$Sn$_{2}$ is 3.2 $\mu\Omega$cm at 300 K, which is almost 20 times higher
than that of typical itinerant-ferromagnets such as Fe and Ni. The anomalous
Hall coefficient $R_{{\rm s}}$ is 6.7$\times10^{-9}$ $\Omega$cm/G at 300 K,
which is three orders of magnitude larger than that of pure Fe. $R_{{\rm s}}$
obeys an unconventional scaling to the longitudinal resistivity, $\rho_{xx}$,
of $R_{{\rm s}} \propto \rho_{xx}^{3.3}$. Such a relationship cannot be
explained by the skew and/or side-jump mechanisms and indicates that the origin
of the anomalous Hall effect in the frustrated magnet Fe$_{3}$Sn$_{2}$ is
indeed extraordinary.
