Abstract: Strategy innovation, management innovation, and product innovation are three most important types of firm innovation. However, our understanding of the relationships among these types of innovation and their impacts on firm performance is limited. Moreover, it is still unknown how firms' ties with competitors can impact the relationships among these three types of innovation. This study, therefore, aims to address these two research gaps. The empirical results from a survey of 247 firms operating in China show that (1) both the influences among these three types of innovation and the impacts of radical and incremental product innovation on firm performance are not equal; and (2) competitor ties play significant roles in the relationships among these three types of innovation. This study contributes to the cross-disciplinary innovation research and innovation management practice.