We construct a new firm-level climate policy uncertainty perception using textual data from the annual reports of Chinese listed firms, and investigate the effect of climate policy uncertainty perception on the cost of equity capital. The empirical results indicate that climate policy uncertainty perception significantly increases the cost of equity capital. The effect is more pronounced in firms with fewer green innovation activities, weaker ESG (Environmental, Social and Governance) performance and private ownership. We further reveal that climate policy uncertainty perception affects the cost of equity capital by increasing corporate risk and lowing investor confidence. Our study constructs a novel measure of climate policy uncertainty at the firm level, and enhances the understanding of the economic consequences of climate policy uncertainty.