In this paper, we investigated the existence of 4-(q+1,7,λ) designs with block-transitive automorphic group PGL(2,q), and the computer algorithm to construct the block-transitive 4-(v,k,λ) designs from PGL(2,q). We also constructed some 4-(q+1,7,λ) designs, in which the parameters can be given and can admit block-transitive automorphic group PGL(2,q).