The financialization and international influence of China's crude oil market are increasing with the listing of China's crude oil futures (INE). In this context, we use the time-frequency connectedness network model to analyse the dynamic spillover effect between Chinese crude oil futures and sector stock indices, and compare it with American crude oil futures (WTI), where the study period includes the COVID-19, the European energy crisis, the Russia-Ukraine conflict and its like. The empirical results demonstrate that the total spillover effect of the crude oil and stock markets is mainly generated by high frequency (1–5 days). Extreme events in crude oil markets such as the Saudi Arabia oil field attack and the negative WTI price led to significant changes in the connectedness network of the system, increasing spillover risk and reducing system stability, but it recovers quickly. Moreover, the heterogeneity of spillover effect from crude oil futures to sector stock indices exists with energy industry and crude oil market the strongest, and meanwhile the spillover effects between crude oil and sector stock indices are smaller than those among sector stock indices in general. Further, China's sector stocks are more closely related to INE (crude oil futures listed on Shanghai International Energy Exchange) than WTI. Specifically, the spillover effect between WTI and INE is asymmetric, that is, the spillover effect from WTI to INE is significantly stronger than from INE to WTI. Finally, Dynamic portfolio weights indicate that assets with low connectedness are beneficial for balancing risk and return. These new findings suggest some useful implications: Regulators should pay close attention to cross-market risk and abnormal vibration of INE, and stock investors in China had better not regard crude oil futures as a hedging market.