  We study the quantum Hall effect(QHE) on the Kagom\'{e} lattice with
anisotropy in one of the hopping integrals. We find a new type of QHE
characterized by the quantization rules for Hall conductivity
$\sigma_{xy}=2ne^{2}/h$ and Landau Levels $E(n)=\pm v_{F}\sqrt{(n+1/2)\hbar
Be}$ ($n$ is an integer), which is different from any known type. This phase
evolves from the QHE phase with $\sigma_{xy}=4(n+1/2)e^{2}/h$ and $E(n)=\pm
v_{F}\sqrt{2n\hbar Be}$ in the isotropic case, which is realized in a system
with massless Dirac fermions (such as in graphene). The phase transition does
not occur simultaneously in all Hall plateaus as usual but in sequence from low
to high energies, with the increase of hopping anisotropy.
