A weighted stock network model of stock market is presented based on the complex network theory. The model is a weighted random network, in which each vertex denotes a stock, and the weight assigned to each edge is the cross-correlation coefficient of returns. Analysis of A shares listed at Shanghai Stock Exchange finds that the influence-strength (IS) follows a power-law distribution with the exponent of 2.58. The empirical analysis results show that there are a few stocks whose price fluctuations can powerfully influence the price dynamics of other stocks in the same market. Further econometric analysis reveals that there are significant differences between the positive IS and the negative IS.