A digraph G is said to be primitive if there exists a positive integer P such that for each ordered pair of vertices u and ν ,there is a walk oflength P from u to v.Let Pn(d) be the set ofall primitive digraphs oforder n(n≥3)with exact d vertices having loops,LG(k) be the k-common consequent (k-c,c.)of primitive digraph G,2≤k≤n,and L(n,d ,k)=max{LG(k)| G ∈ Pn (d)},In this paper,the bound of k-common consequent,namely,n-「d/2」≤L (n,d,k)≤n-1,1≤d≤n,is obtained.