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[en] In this paper, we introduce a modified small-world network added with new links with preferential connection instead of adding randomly, then we apply Bak-Sneppen (BS) evolution model on this network. Several dynamical character of the model such as the evolution graph, f0 avalanche, the critical exponent D and τ, and the distribution of mutation times of all the nodes, show particular behaviors different from those of the model based on the regular network and the small-world network.