Applying the theory of statistical physics systems – the voter model, a random stock price model is modeled and studied in this paper, where the voter model is a continuous time Markov process. In this price model, for the different parameters values of the intensity λ, the lattice dimension d, the initial density θ, and the multivariate set ( θ, λ), we discuss and analyze the statistical behaviors of the price model. Moreover, we investigate the power-law distributions, the long-term memory of returns and the volatility clustering phenomena for the Chinese stock indices. The database is from the indices of Shanghai and Shenzhen in the 6-year period from July 2002 to June 2008. Further, the comparisons of the empirical research and the simulation data are given.