Under the background of economic integration, studying the risk spillover effect of domestic and foreign carbon trading markets is of great significance to investment decision-making, risk management and the healthy development of carbon market. This paper studies the dynamic dependency structure of EU and domestic carbon trading market by combining time-varying copula function and generalized auto-regressive conditional heteroscedasticity (GARCH) model. On this basis, it uses copula CoVaR model to study the risk spillover effect of EU carbon market on domestic carbon market. The results show that: (1) The optimal time-varying copula functions depicting the dynamic dependent structure of EU futures market and China's carbon markets in Beijing, Shanghai, Hubei and Shenzhen are different, reflecting the heterogeneous characteristics of China's regional carbon market. (2) Further, based on Copula CoVaR model, the risk spillover effect of EU and domestic carbon market is obtained. It is found that EU futures have risk spillover effect with Beijing, Shanghai and Hubei carbon market, and there is no risk spillover phenomenon with Shenzhen carbon market. Based on the above conclusions, this paper puts forward relevant policy suggestions to prevent carbon market risks.