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　heavytailed　features　in　real　data.　Shanghai　Stock　Market　Index　as　a　real　example　illustrates　the　results.　©　Sila　Science.