Previous studies on the impact of customer concentration on firm-level outcomes mainly focus on financial and operational variables, and the influence of a concentrated customer base remains controversial. As one of the important issues of responsible and sustainable operations management, corporate social responsibility (CSR) has garnered increasing attention of scholars in recent years. However, research on CSR antecedents is far less than the studies of its outcomes, and few studies investigate what determines CSR engagement from buyer-supplier relationship perspective. Using a large sample panel data from Chinese publicly listed firms between 2010 and 2019, we find that a concentrated customer base is negatively associated with suppliers' CSR performance. Our results still hold after a series of robustness checks. Next, the results show that customer concentration is also negatively correlated with CSR's five dimensions, but the negative impact on non-core stakeholders is more significant than that on core stakeholders. Further, the mechanism analysis reveals that profitability and financial constraints are two potential transmission mechanisms in the linkage between customer concentration and CSR performance. Finally, we find that the negative impact is more salient when a supplier with higher transparency. Overall, our study suggests that a close relationship between a supplier and its major customers may impede the supplier's incentives to do good things, and a supplier may weigh benefits and costs to strategically adjust its CSR behaviour as a response to customer risk. These findings have significant implications for suppliers, customers, and regulators.