In this paper, we employ the dynamic copula approach to explore the dependence structure between WTI oil and Chinese energy stock index (300ENI). We first use the AIC (Akaike Information Criteria) together with the binary segmentation procedure to detect the change points of copula families and copula parameters, which extend the existing time-varying copula method. Then we can get the optimal copula between WTI oil and 300ENI for each time period, and analyze the dependence between them combining with the national and international economic environment. We find that the recession of both the international oil market and Chinese energy stock market causes the significant concordance and symmetric tail dependence. The asymmetric dependence turns out to be in Chinese economic recession and recovery time. Furthermore, we apply our results to analyze the effectiveness of hedging WTI oil using 300ENI. Results show that the hedging is more effective in China's sluggish time than in economic boom. Finally, our economic cycle analysis shows that different economic situation pairs of WTI oil and Chinese energy stocks exhibit different tail dependency, which could be used to predict the market future and provide market participants and policy makers with some suggestions on investment, hedging and decision making. • The dynamic copula with change in parameters and types is modeled. • A new method of applying Akaike Information Criterion into binary segmentation procedure is proposed. • The relationship between WTI oil prices and 300ENI returns have been studied. • Different economic state pairs of two markets exhibit different concordance and tail dependency. • The proposed model is applied to calculate the hedge ratio and hedging effectiveness of 300ENI against the WTI oil risk.