This paper investigates the risk spillover between the crude oil market (West Texas Intermediate and Brent) and the Chinese stock market (Shanghai Stock Exchange) by using the marginal expected shortfall model and Beta-skew-t-exponential generalized autoregressive conditional heteroscedasticity-extreme value theory model combined with the copula-conditional value-at-risk (CoVaR) model covering the period from January 4, 2007 to June 30, 2014. Further, the full data sample is divided into a turbulent period and a calm period to capture the risk spillover effect across different economic scenarios. The results indicate that the upside CoVaRs and the downside CoVaRs are asymmetric over the sample period, and that the upside CoVaRs during the turbulent, calm and complete periods are greater than the downside CoVaRs. The results on marginal expected shortfall and ∆CoVaRs show that there are bidirectional asymmetric risk spillover effects between the crude oil market and the Chinese stock market and that the risk spillover effect from the Chinese stock market to the crude oil market is greater than that of from the crude oil market to Chinese stock market.