With the increasing importance of leadership in project-based organizations, innovation is essential for the sustainable development of construction projects. Since few studies have explored the relationship between leadership and innovation in construction projects, this study fills this research gap and makes a significant theoretical contribution to the existing body of literature. Based on a knowledge-rated and resource-based view, this study aims to investigate various effects of different types of leadership on innovation performance in a construction project-based organization. Therefore, a theoretical model was constructed to explore the mediation mechanism and boundary condition of different types of leadership to improve innovation. The theoretical model was validated with empirical data covering project managers and engineers from the project-based organization in China via regression analysis and path analysis. The results show that transformational leadership and transactional leadership have some positively significant effects on knowledge sharing and innovation performance. Meanwhile, knowledge sharing partially mediates the relationship between transformational leadership and/or transactional leadership and innovation performance. Additionally, by considering different levels of social capital, transformational leadership is likely to have a strong positive impact on innovation performance through knowledge sharing. Our findings ensure a better understanding of the role of leadership, knowledge management, and social capital in the innovation process of construction projects. Therefore, project managers should promote a higher stimulation of a leadership behavior, encouraging knowledge management, and establishing the social capital, thus improving the innovation performance in the project-based organizations in construction projects.