  Let $G$ be a flag-transitive automorphism group of a $(v,k,\lambda)$
symmetric design $\mathcal{D}$ with $k>\lambda(\lambda-2)$. O'Reilly Regueiro
proved that if $G$ is point-imprimitive, then $\mathcal{D}$ has parameters
$(v,k,\lambda)=(\lambda^2(\lambda+2),\lambda(\lambda+1),\lambda)$. In the
present paper, we consider the case that $G$ is point-primitive. By applying
the O'Nan-Scott Theorem, we prove that $G$ must be of affine type or almost
simple type.
