Since Bollerslev(1986), the GARCH model has been popular in analysing the volatility of the financial time series. In real data analysis, practitioners conventionally put the normal assumption on the innovation random variables of the GARCH model, which is often violated. In this paper, we analyse the domestic financial data based on the GARCH(1,1) model and among existing normality tests, perform the Jarque-Bera test based on the residuals. It is shown that the innovation based on the GARCH(1,1) model dose not follow the normality assumption.