Global geopolitical risks matter to China's energy futures market. Through a three-stage research framework combining higher-order moment (third- and fourth-order moments), time-frequency spillover model, and the random forest technique, we identify the influence of global energy countries' geopolitical risks on China's energy futures spillovers under different time horizons. Our third-order moment (skewness) spillover results indicate that crude oil and fuel oil futures primarily play the role of net transmitters in the short-term time scale, while coking coal and bitumen futures are mainly net recipients. In the medium- and long- term time scales, however, thermal coal and fuel oil are stable net recipients. For the fourth-order moment (kurtosis) spillovers, the crude oil consistently acts as the transmitters across all time horizons, with a relatively significant net spillover value. Moreover, Russia's geopolitical risk has the most prominent impact on spillovers in China's energy futures market, followed by Saudi Arabia. Additionally, Russia and Saudi Arabia are more likely to impact upside and downside market spillovers, respectively. These results provide some implications for different types of investors and policy makers.