Abstract: The problem of minimizing broadcasting time in network was considered and a model of ki broadcasting was given,that is,for each vertex vi ∈V this vertex vi has the information can transmit its information to at most ki neighbors per a unit time.The objective of the problem is to minimize the broadcasting time such that all vertex in the network obtain this information.It is pointed out that the problem is NP-completeness.A polynomial time algorithm was constructed to determine the minimal broadcasting time from the fixed vertex u and the broadcasting center in a hierarchical network is found.