In this paper, we study the flag-transitive quasi-symmetric 2- \((v,k,\lambda )\) designs. Let \({\mathcal {D}}\) be a quasi-symmetric 2-design with intersection numbers \(x=0\) and \(2\le y\le 10\) , which we assume throughout. We prove that if \(G\le Aut({\mathcal {D}})\) is flag-transitive and point-imprimitive, then \({\mathcal {D}}\) has exactly two possible parameter arrays \((b,v,r,k,\lambda ,c,d)\) , which we explicitly determine. Furthermore, we show that G is point quasi-primitive if and only if it is point-primitive. Moreover, if G is flag-transitive and point-primitive on a 2- \((v,k,\lambda )\) design \({\mathcal {D}}\) with socle \(\textrm{PSL}_2(q)\) \((q \ge 4)\) , then \(r\mid f q (q-1)\) , \(p\mid r\) , and \(q\mid (y-1)r\) , where \(q = p^f\) . In particular, if \(gcd(r,\lambda )=1\) , then \({\mathcal {D}}\) is the unique 2-(8, 4, 3) design up to isomorphism.
