In complex networks, node degree values are limited by some practical factors. The saturation of node degree, which is a function of network evolution time, is defined first. We propose a novel evolving bipartite network model based on preferential attachment in local-world, which is generated by node saturation restrictions, not new node selection. So we also call it local-world-like model. However, the numerical simulation results display that the degree distribution does not obey the power-law distribution. We find that the degree value interval of this local-world-like bipartite network is small. There is no hub node. In addition to these, we analyze mixing coefficient of the network and find that the assortativities of the network are different when the network is generated by different initial parameters Such a result accords with our simulated result.