Prior studies on corporate social responsibility (CSR) and innovation suggest either a competing or a complementary relationship between CSR and spending on research and development (R&D) activities. In this study, we unravel this puzzle by theorizing an inverted U‐shaped relationship between CSR in general and corporate philanthropy (CP) in particular, and R&D spending. Drawing mainly on stakeholder theory, we suggest that CP, by securing stakeholders’ support differently at different levels of spending, would first increase and then reduce R&D spending. Evidence from Chinese publicly traded companies during 2006–2015 well supports our arguments. In addition, we find this inverse U‐shaped non‐linear relationship between CP and R&D spending to be strengthened by firm visibility and weakened by firm size. This study has important theoretical and practical implications. Copyright © 2017 John Wiley & Sons, Ltd and ERP Environment