Abstract: Based on the discussion of method and process for the distribution of Stock Index Rate of Return and nonlinear testing,this paper makes an empirical research on the General Index Rate of Return in the stock markets of Shanghai and Shenzhen.It first applies the basic statistic Kolmogorov-Smirnov testing to analyze the Rate of Return,which sequentially follows the Normal Distribution;then it uses the Autocorrelation Function to test the Rate of Return sequence,which is a nonlinear process.