The research on the application of parametric and nonparametric ARCH model to the volatility of Shanghai and Shenzhen index from 15 May, 2007 to 9 March, 2012 in our country reached the following conclusions: the estimation precision and prediction results of the volatility of Shanghai stock index obtained by nonparametric ARCH model is superior to obtained made by the parametric AＲCH model, while as for the volatility of Shenzhen component index the result of nonparametric estimation precision is lower than that of the ARCH model, with the predicted results alike; in general,  the mean square error of both methods is very small.  This article applies nonparametric ARCH model to the description of the Shanghai and Shenzhen index fluctuation, and objectively obtained the related conclusion and suggestions, which lays a foundation for the nonparametric ARCH model, as an alternative measure,to be applied to the research on the volatility of financial assets.