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Let $\mathcal D$ be a nontrivial symmetric $(v,k,\lambda)$ design, and $G$ bea subgroup of the full automorphism group of $\mathcal D$. In this paper weprove 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 $(15, 8, 4)$.

Classification of flag-transitive primitive symmetric $(v,k,\lambda)$ designs with $PSL(2,q)$ as socle