This paper proposes the heterogeneous volatility spillover-conditional autoregressive range (HVS-CARR) model for modeling and forecasting Chinese crude oil futures’ volatility, which is a common measure of Chinese crude oil market risk. The proposed HVS-CARR model is able to account for extreme-value information as well as the time-varying volatility spillovers from international to Chinese crude oil futures markets, thereby enhancing the assessment of Chinese crude oil market risk. Our empirical results show the presence of time-varying volatility spillovers from the West Texas Intermediate futures market to the Shanghai International Energy Exchange crude oil futures market, and they indicate that the spillover spiked during the 2020–23 Covid-19 pandemic, reflecting a period of aggravated Chinese crude oil market risk. In particular, we observe that the proposed HVS-CARR model outperforms a variety of competing models in terms of out-of-sample volatility forecasting, including the return-based generalized autoregressive conditional heteroscedasticity (GARCH) model, the GARCH-mixed-data sampling (GARCH-MIDAS) model and the HVS-GARCH model, as well as the range-based CARR model and the CARRMIDAS model, highlighting the improved ability of our proposed HVS-CARR model to quantify and forecast Chinese crude oil market risk. Finally, we confirm that incorporating extreme-value information and time-varying volatility spillover effects into a volatility-timing strategy leads to substantial economic gains.