The relations between carbon and energy market is a hot topic but little research has focused on the time-varying spillover in a quantitative way. This paper employs the method introduced by Diebold and Yilmaz (2012) which constructs the spillover index by variance decomposition of the prediction error. The results reveal the asymmetric spillover effect between two types of markets in return and volatility series. Among three energy markets including WTI oil, Brent oil and natural gas markets, WTI oil market transmits the strongest spillover effect to the system, and the spillover effect of natural gas to carbon market is also prominent. Then, we adopt the rolling window technique and detect the time-variation property in the spillover effect. It turns out that some major policy changes and events can cause great changes in spillover index. Furthermore, we study the spillover under extreme conditions and our results show the significant mean spillover (volatility spillover) from oil (natural gas) market to the carbon market. (C) 2018 Elsevier Ltd. All rights reserved.