With the rapid spread of carbon trading in the global economy, the interactions of prices between carbon (or clean/renewable energy) and traditional fossil energies such as coal and oil have raised growing attention, but little research have discussed their dynamic volatility spillover and time-varying correlation. The purpose of this study is to investigate these issues, for the weekly data of EUA futures, Biofuel and Brent oil prices from 25 October 2009 to 5 July 2020. We employ the VAR-GARCH model with the BEKK specification. Our results are summarized as follows. At first, we identified the sudden changes and the volatility persistence in the three markets, and also confirmed that the volatility of the markets has changed significantly over time. Secondly, we find that there are a weak volatility spillover effect among the three markets, while a strong spillover effect between the EUA and Brent oil markets. Lastly, in financial markets, the EUA can be used as a hedging portfolio for the Biofuel and Brent oil markets. These results can help investors to well compose their portfolios and manage their investment risks, and help potential pollutant emission sources to join in carbon market in a cost-effective way.