In recent years, the extreme risk events occurred frequently in the financial market have not only brought huge losses to investors and inflicted heavy losses on the market, but also posed a severe challenge for the traditional effective market hypothesis. These extreme risk events are often accompanied by sudden plummeting of liquidity. Different from the efficient market hypothesis(EMT), firstly, this paper studies the nonlinear fluctuation characteristics and causes of contracts with different maturity periods in China stock index futures market under the framework of fractal market theory and using the multifractal detrended fluctuation model Secondly, under the framework of the fractal market theory, the existence of the liquidity spillover effect between the stock index futures and spot is tested, the direction, intensity, and contribution of spillover between stock index futures and spot are analyzed. Finally, there is a robustness test. The study finds that both stock index futures and stock index spot in China have obvious nonlinear fractal fluctuation characteristics, and stock index futures have higher degree of multifractal, the characteristics are related to correlated multifractal and distributed multifractal; the longer the maturity period of the stock index futures contract, the lower the multifractal degree; there are significant asymmetric liquidity spillover effects between the stock index futures and spot; the multifractal degree has an important influence on the intensity and contribution of the liquidity spillover effect, and the multifractal degree is inversely proportional to the intensity of liquidity spillover and the contribution of spot to futures fluctuations.