Abstract: The research on the long memory of returns and volatility of stock index futures yield can reflect the efficiency of the market. This paper researched the long memory of returns and volatility of CSI 300 index futures by applying ADF-KPSS test,Autocorrelation test and R/S test method. The results showed that the returns series of CSI 300 stock index futures lack significantly long memory, but the volatility series of CSI 300 stock index have significantly long memory. The long memory of volatility implies that the impact of events and news on stock index futures market in China will not disappear immediately, and might have long-term and far-reaching influence on the market. It also means that the effectiveness of stock index futures market in China needs to be strengthened. We need to strengthen market building from the aspects of information disclosure and training diversification of investors to eliminate the impact of long memory on the healthy development of stock index futures market in China. Finally, the article used FIGARCH model to measure the long memory of volatility series to provide a reference for subsequent research on the stock index futures.