During the high risk period, the yield rate series of stock of index has more obvious fat-tail phenomenon, Setting the residuals for fat-tail distribution of these GARCH models is superior to the models with normal distribution and t distribution. According to the five kinds of loss functions, GARCH model、EGARCH model and GJR-GARCH model are compared based on fat-tail distribution, the conclusion is that GARCH(1, 1) model with briefer structure has a better prediction ability in the high risk period.