The purpose of this study is to investigate the relationship between competition and innovation. This complex relationship have been attracted the attention for several decades. This research adopts the patent and R&D turnover as the proxy for the innovation outputs; the HHI is the proxy for the competition. This study explores the relationship in the Taiwanese service sector by using the Panel, Poisson, and Negative-binominal regressions. The results indicate that the relationship between innovation and competition may be a mild U relationship. The contribution of the study helps clarify the relationship in the Taiwanese service sector.