Introduction: The climate issue is a huge challenge facing humanity today, and the carbon market, as a significant institutional innovation to address climate change, can play a critical role in reducing carbon emissions. Aim: This research aimed to thoroughly identify and analyse the impact of climate policy uncertainty (CPU) on carbon trading prices (CTP). Method: This paper applies wavelet-based quantile-on-quantile regression to quantify the marginal impact of CPU on CTP at various quantiles of both variable distributions across different periods, fully identifying the heterogeneity and full-distribution characterisation of the dynamic response of CTP to CPU. Findings: The evidence shows a nonlinear and asymmetric correlation between CPU and CTP at different time scales, but the direction cannot be determined. The reason is that the government's attitude towards climate issues may change at different times. When climate policy releases are tilted in favour of controlling carbon emissions, it leads to a boom in the carbon market and thus increases CTP. In addition, a stable CPU will encourage innovation in lowcarbon technologies, but the potential carbon emissions from the construction and manufacture of new technologies in the short term cannot be ignored. Originality and value: It provides information for carbon market participants to help them make sound and scientific investment decisions. Investors can grasp the trend of CTP according to CPU and invest in carbon credit assets during the period of high CPU for long-term risk diversification and wealth preservation.