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Providing a scientific basis and method to ensure the smooth functioning of the Chinese crude oil market would be hugely significant to China's future economic development and security. To this end, attempts have been made to both internationalize the Shanghai crude oil market and minimize financial risks. This paper selects three crude oil markets (INE, WTI and Brent) and five Chinese financial markets (the futures, bond, fund, stock and foreign exchange markets) as the research objects. The Diebold and Yilmaz spillover index model and the multifractal asymmetric detrended cross-correlation analysis (MF-ADCCA) method are used to study the volatility spillover effect and the asymmetric cross-correlation between crude oil markets and financial markets. When the volatility spillover effect and the asymmetric relationship that exists between the financial markets are examined, the volatility spillover of the oil market to the financial market is found to be significantly higher than that of the financial market to the oil market. In particular, the spillover effect was even more significant from late-2019 to early-2020. Analysis demonstrates an asymmetric cross-correlation between crude oil markets and the abovementioned five Chinese financial markets. In particular, the impact of the Chinese crude oil market on the stock market is greatest, especially with respect to the Brent and WTI crude oil markets. Except for the bond market, when the INE and Brent markets are increasing, the risk exposure to financial markets is more significant. Among financial markets, INE-Bond market asymmetry is stronger than WTI-bond market asymmetry, but weaker than that of the Brent-Bond market when there are large fluctuations. [ABSTRACT FROM AUTHOR]