  Let $\Omega$ be a $m$-set, where $m>1$, is an integer. The Hamming graph
$H(n,m)$, has $\Omega ^{n}$ as its vertex-set, with two vertices are adjacent
if and only if they differ in exactly one coordinate. In this paper, we provide
a proof on the automorphism group of the Hamming graph $H(n,m)$, by using
elementary facts of group theory and graph theory.
