With　the　development　of　nonlinear　science,　the　existence　of　long　memory　in　the　financial　market　volatility　has　been　found,　which　is　inconsistent　with　the　weak　form　of　Efficient　Market　Hypothesis.　With　the　brief　introduction　of　Heterogeneous　Market　Hypothesis　and　Fractal　Market　Hypothesis,　the　long　memory　behavior　of　Shanghai　Stock　Index＇s　returns　volatility　is　tested,　based　on　H/S　analysis　and　GPH　method.　By　using　the　realized　volatility　to　measure　the　true　volatility　and　combining　with　the　analysis　of　ARFIMA-RV　and　HAR-RV　model,　Shanghai　Stock　Index＇s　RV　series＇　long　memory　behavior　is　confirmed,　and　HAR-RV　model　behaves　better　in　the　prediction　of　volatility.　©2010　IEEE.