Among the many reasons to encourage enterprises to implement green innovation, external factors such as market mechanisms and policy regulation both have the greatest probability of failure. Therefore, the idea of exploring ways to promote green innovation from internal factors has gradually attracted attention. This study is based on an internal perspective to explore the relationship between board size, openness, and green innovation by using data from the heavily polluting enterprises listed in China’s A-share market from 2015 to 2020. The regression results show that board size has a significant positive impact on green innovation, and the openness breadth plays a partial mediating role. This indicates that more board members are conducive to the implementation of green innovation strategies, as well as expanding the innovation openness breadth, so as to obtain external knowledge and resources to promote green innovation. Through further heterogeneity analysis, we found that the above relationship is more significant in state-owned enterprises. Finally, this study provides new theoretical evidence for the debate over whether board size promotes or inhibits green innovation. Furthermore, it provides a path and practical guidance for enterprises to implement green innovation more effectively by relying on their directors’ networks and increasing their own openness.