Abstract: In traditional BA scale-free networks,the maximum degree of nodes increases unlimitedly with the scale of networks,which causes some hub nodes with large degree existing in the networks.Considering the cost of constructing the real networks,the maximum degree of nodes is limited.According to the growing rules of the BA network,this paper proposes a limited-maximum-degree BA network model,called LBA network,then further studies the average path length,clustering coefficient and degree distribution of LBA network under different values of the restriction of maximum degree K,and compares them with thestatistical properties of the neighbor network,the random network and the BA network.Research shows that the generated LBA network is similar to the neighbornetwork when K is close to the network average degree,LBA network propertiesare close to the random network when K is about 2 times of the network average degree,and the statistical properties of LBA network are close to the original BA scale-free network with a relative larger K.