  We investigate the chiral edge states in the two-dimensional ferromagntic
kagom\'{e} lattice with spin anisotropies included. The system is periodic in
the $x$ direction but has two edges in the $y$ direction. The Harper equation
for solving the energies of edge states is derived. We find that there are two
edge states in each bulk energy gap, corresponding to two zero points of the
Bloch function on the complex-energy Riemann surface (RS). The edge-state
energy loops parametrized by the momentum $k_{x}$ cross the holes of the RS.
When the Fermi energy lies in the bulk energy gap, the quantized Hall
conductance is given by the winding number of the edge states across the holes,
which reads as $\sigma_{xy}^{\text{edge}}$=$-\frac{e^{2}}{h}% $sgn$(\sin\phi)
$, where $\phi$ is the spin chiral parameter (see text). This result keeps
consistent with that based on the topological bulk theory.
