  Fuglede's conjecture states that for a subset $\Omega$ of a locally compact
abelian group $G$ with positive and finite Haar measure, there exists a subset
of the dual group of $G$ which is an orthogonal basis of $L^{2}(\Omega)$ if and
only if it tiles the group by translation. In this paper, we prove a
divisibility property for a set in $\mathbb{Z}_{p}\times\mathbb{Z}_{p^{n}}$.
Then using the divisibility property and equi-distributed property, we prove
that Fuglede's conjecture holds in the group
$\mathbb{Z}_{p}\times\mathbb{Z}_{p^{n}}$.
