This study explores the dynamic relationships among trade policy uncertainty (TPU), climate policy uncertainty (CPU) and crude oil prices (WTI) through Granger causality, TVP-VAR and TVP-VAR-DY analysis. It is found that there is a two-way causality between TPU and WTI, CPU and WTI, while a one-way causality from TPU to CPU. Based on these results, the time-varying relationships are further analyzed, revealing a negative interaction between TPU and WTI, a positive relationship between CPU and WTI, and a positive effect of TPU on CPU. Moreover, these relationships are time-varying and exhibit distinct patterns at different time points. For instance, the negative interaction between TPU and WTI is strongest during the 2008 financial crisis, while the positive interaction between CPU and WTI is most significant during the COVID-19 pandemic. TPU shocks have an increasing positive impact on CPU and the effect during the short run is the most significant, which is strongest during the Paris Agreement in 2016. Finally, the spillover effect results suggest that CPU is a net spillover receiver, while TPU and WTI are net spillover transmitters.