We aim to explore whether board gender diversity—specifically, women directors representing institutional ownership—improves the sustainability development of listed firms by affecting corporate social responsibility (CSR) policies. Moreover, among female directors representing institutional shareholders, we can differentiate between those working for banks and insurance companies (pressure‐sensitive female institutional directors) and those working for mutual funds, investment funds, pension funds, and venture capital firms (pressure‐resistant female institutional directors). The effect of these categories of directors on CSR policies is also analysed. Our evidence suggests that women directors representing institutional ownership positively affect CSR policies, which is the same as for pressure‐resistant female institutional directors, and pressure‐sensitive institutional directors do not impact CSR policies. This research provides a new framework for the role played by certain types of female directors (female institutional directors, female pressure‐sensitive directors, and female pressure‐resistant directors) in relation to CSR policies, and thus, it may help policymakers to promote CSR policies and to take action to promote responsible behaviour among listed firms.