  The chiral edge states and the quantized Hall conductance (QHC) in the
two-dimensional kagom\'{e} lattice with spin anisotropies included in a general
Hund's coupling region are studied. This kagom\'{e} lattice system is periodic
in the $x$ direction but has two edges in the $y$ direction. Numerical results
show that the strength of the Hund's coupling, as well as the spin chirality,
affects the edge states and the corresponding QHC. Within the topological edge
theory, we give the expression of the QHC with the winding number of the chiral
edge states on the Riemman surface. This expression is also compaired with that
within the topological bulk theory and they are found to keep consistent with
each other.
