["International Journal of Finance &Economics, EarlyView. ", "\nABSTRACT\nAmid growing global environmental challenges, supply chains have become a critical conduit for the transmission of environmental pressures. However, existing research presents theoretical divergences regarding the effectiveness of customer environmental pressure transmission, primarily due to the neglect of customers' subjective cognitive appraisal of such pressures. Grounded in the cognitive appraisal theory of stress, this study constructs an environmental pressure perception index by analysing the tone of annual report texts, aiming to elucidate the impact and underlying mechanism of customer environmental pressure perception on suppliers' greenwashing. Using a sample of Chinese A‐share listed companies from 2009 to 2022, we find that customer environmental pressure perception significantly curbs the extent of supplier greenwashing. Mechanism analysis reveals that customer environmental pressure perception inhibits greenwashing through two pathways: improving the quality of suppliers' environmental information disclosure and increasing their environmental investments, with these two pathways exhibiting a chain‐mediating effect. Heterogeneity analysis indicates that this inhibitory effect is more pronounced when customers exhibit high information disclosure quality, when suppliers are private enterprises, or when supply chain dependency is strong. By emphasising the pivotal role of subjective perception rather than objective pressure, this study not only offers a cognitive appraisal perspective to explain theoretical disputes concerning pressure transmission within supply chains, but also provides important implications for enterprises and policymakers in effectively mitigating greenwashing and enhancing the overall green performance of supply chains.\n"]