  Let $p$ and $q$ be distinct odd primes. Let $\Gamma=(V(\Gamma), E(\Gamma))$
be a non-Cayley vertex-transitive graph of order $pq.$ Let $G\leq \Aut(\Gamma)$
acts primitively on the vertex set $V(\Gamma)$. In this paper, we show that $G$
is uniprimitive which is primitive but not 2-transitive and we obtain some
information about $p, q$ and the minimality of the Socle $T=\soc(G).$
