  A subset $\mathcal{F}$ of a finite transitive group $G\leq
\operatorname{Sym}(\Omega)$ is intersecting if for any $g,h\in \mathcal{F}$
there exists $\omega \in \Omega$ such that $\omega^g = \omega^h$. The
\emph{intersection density} $\rho(G)$ of $G$ is the maximum of $\left\{
\frac{|\mathcal{F}|}{|G_\omega|} \mid \mathcal{F}\subset G \mbox{ is
intersecting} \right\}$, where $G_\omega$ is the stabilizer of $\omega$ in $G$.
In this paper, it is proved that if $G$ is an imprimitive group of degree $pq$,
where $p$ and $q$ are distinct odd primes, with at least two systems of
imprimitivity then $\rho(G) = 1$. Moreover, if $G$ is primitive of degree $pq$,
where $p$ and $q$ are distinct odd primes, then it is proved that $\rho(G) =
1$, whenever the socle of $G$ admits an imprimitive subgroup.
