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The statistical analysis of Chinese stock market fluctuations modeled by the interacting particle systems has been done in this paper. The contact process of the interacting particle systems is presented in this paper, where it is a continuous time Markov process, one interpretation of this model is as a model for the spread of an infection. Based on the contact process, a new stochastic stock price model of stock markets is modeled. From it, the statistical properties of Shenzhen composite Index are studied. The data of Shenzhen Stock Exchange (SZSE) Composite Index is analyzed, and the corresponding simulation is made by the computer computation, and we further investigate the statistical properties, fat tails phenomena and the power-law distributions of returns. The methods of Skewness-Kurtosis test, Kolmogorov-Smirnov test are applied to study the fluctuation behavior of the returns for the stock price and index.