In this article, we study 2-designs with λ = 2 admitting a flag- transitive and point-primitive almost simple automorphism group G with socle X a finite simple classical group of Lie type. We prove that such a design belongs to an infinite family of 2-designs with parameter set ((3n − 1)/2, 3, 2) and X= PSLn(3) for some n 3, or X = PSL2(q) with point-stabiliser D2(q+1)/ gcd(2,q−1), or it is isomorphic to the 2-design with parameter set (6, 3, 2), (7, 4, 2), (10, 4, 2), (11, 5, 2), (28, 7, 2), (28, 3, 2), (36, 6, 2) or (126, 6, 2).
