Recently, there has been a lot of interest in modeling real data with a heavy tailed distribution. A popular candidate is the so-called generalized autoregressive conditional heteroscedastic (GARCH) model. Unfortunately, the tails of normal GARCH models are not thick enough in some applications. In this paper, we propose a GARCH model with normal scale mixture innovations, the parameters estimation procedure using EM algorithm is also provided. It is shown that GARCH models with normal scale mixture innovations have tails thicker than those of normal GARCH models. Therefore, the GARCH models with normal scale mixture innovations are more capable of capturing the heavy-tailed features in real data. Shanghai Stock Market Index as a real example illustrates the results.