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The BA model and BA extend model described the number of nodes linked, but the researchers believe the nodes have the highest number of links if the timeframe is enough long. However, the real system not only depend on timeframe, hence, we proposed a new network evolving model which has attractive factor, the number of links of nodes have relate with attractive factor. If new nodes have enough attractive factors, it can acquire the highest number of links in short time, so it can beyond the old node. The evolving progress of model is simulated by computer, the degree distribution, clustering, average path of BA model and attractive factor model are gotten in the same network scale. The simulation results indicate the degree distribution of nodes under attractive factor present power-law distribution, which has similar with BA model. The correctness of theory is verified by simulation analyses.