In this article, we study flag-transitive automorphism groups of non-trivial symmetric (v,k,λ) designs, where λ divides k and k > λ 2 . We show that such an automorphism group is either point-primitive of affine or almost simple type, or point-imprimitive with parameters v = λ 2 (λ+2) and k = λ(λ+1), for some positive integer λ. We also provide some examples in both possibilities.
