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A weighted evolving model of scale-free network is proposed. Our model has been inspired by the weighted network model proposed by Alain Barrat et al. (BBV for shot), which consider the emergences of new links according to Triad Formation and strength preferential selection mechanism. Interactions more easily occur between neighbors with high-strength in our model. The effects of Triad Formation on the structure of our evolving scale-free model were investigated. The evolution of degree, strength, weighted exhibit the power-law distributions. Highly correlated with the degree, the average strength displays scale-free property in our model. The average clustering coefficient exhibits a power-law decay as a function of degree of node. Triad Formation mechanism can distinctly enhance the clustering coefficient of network.