  Let $\mathcal D$ be a nontrivial symmetric $(v,k,\lambda)$ design, and $G$ be
a subgroup of the full automorphism group of $\mathcal D$. In this paper we
prove that if $G$ acts flag-transitively, point-primitively on $\mathcal D$ and
$Soc(G)= PSL(2,q)$, then D has parameters $(7, 3, 1)$, $(7, 4, 2)$, $(11, 5,
2)$, $(11, 6, 3)$ or $(15, 8, 4)$.
