Based on the Merton’s jump diffusion model，two amendments are carried out． Firstly，the counting process ( Poisson process) will be amended by the renewal process with power-law nature． Secondly，the magnitude of the jump has also been given the characteristics of power-law nature． By empirical research，it is found that the model could accurately describe the process of the stock price movement，and get a yield with fat-tailed distribution and volatility clustering． As a basis，the model can be used to more accurately price fi-nancial derivatives products such as options，and also provide effective tools in financial risk management．