Few studies have addressed how customer concentration affects the decision of a firm’s research and development (R&D) strategies and then innovation outcome. Using a sample of China’s listed companies for the period from 2009 to 2017, this study investigates the relationship between customer concentration and enterprise sustainable innovations, as well as how such the relationship changes with economic policy uncertainty. The findings imply that there is a significant inverted-U-shaped relationship between customer concentration and enterprise sustainable innovations. Under a high level of economic policy uncertainty, the advantage of the customer relationship is maximized. In this context, raising customer concentration significantly promotes enterprise sustainable innovations. Customer concentration affects innovations differently as the equity properties, and locations of enterprises vary under different levels of economic policy uncertainty. Thus, the interval of customer concentration conducive to enterprise innovations differs. The results are robust to econometric techniques that control for endogeneity. Overall, our findings suggest that enterprises build and adjust the customer relationship and improve the driving mechanism for sustainable innovations.