Accurate prediction of the volatility of EU carbon emission quota futures is an important foundation for pricing derivative products, portfolio allocation, and risk management. On the basis of the GARCH-MIDAS model involving mixed frequency data sampling, this article considers the spillover effect of Brent crude oil futures market on carbon quota futures market, and incorporates the spillover effect into the prediction of carbon quota futures volatility to construct the VS-GARCH-MIDAS model. Using the monthly realized volatility of Brent crude oil futures as a proxy variable to reflect spillover effects, empirical results indicate the existence of a one-way spillover effect of Brent crude oil futures market on carbon quota futures market. Moreover, the GARCH-MIDAS model considering spillover effects has better in sample fitting performance and stronger out of sample predictive ability than the original GARCH-MIDAS model. To ensure the robustness of this conclusion, this paper also investigates the impact of spillover effects generated by WTI crude oil futures on the volatility of EUA futures, and concludes that the GARCH-MIDAS model considering spillover effects can improve the prediction accuracy of EUA futures volatility.