This paper studies the effectiveness of the CSI 300 index futures markets from the perspective of information efficiency and function efficiency and examines the nonlinear dynamic characteristics of efficiency by using nonparametric methods. For information effectiveness, we find that the price of stock index futures follows a random walk. For function effectiveness, the results show that (1) the average optimal hedge ratio is 0.8702, and the average effective level reaches 86.11%. (2) The error correction mechanism is only supported by stock index futures. The error correction effect only exists in the extreme regime (only 6% of the total observed value). Most of the time (94%), both prices are subject to random walk process. There is no arbitrage trade between futures and spots. (3) Both linear and nonlinear leadership are observed in stock index futures. The nonlinear leadership is mainly reflected in stock index futures. Both leadership types are influenced by institutional changes and significant financial events and evolve over time, which indicates that stock index futures cannot play the dominant role in price discovery. In sum, we conclude that the CSI 300 stock index futures market is effective, despite the flaws in price discovery.