In this paper the classification problem of block-transitive 3-designs is discussed. Let G be the block-transitive automorphism groups of a 3- \((v, 7, \lambda )\) design \(\mathcal {D}\) . If G is point-primitive, using the classification theorem of the primitive permutation groups we get G is affine or almost simple type. If G is point-imprimitive, then G has rank 3, \(v=22\) . Moreover, up to isomorphism there exist 27 3- \((22,7,\lambda )\) designs \(\mathcal {D}\) with \(\lambda \in \{18,48,80,90,180,240,288,360,1440,2016\}\) .
