Team ambidextrous innovation is the foundation of enterprise ambidextrous innovation, and the cognitive characteristics of leader is an important influencing factor of team ambidextrous innovation. However, there is no research that has been discussed on the impact of leaders’ cognitive characteristics on team ambidextrous innovation. Based on the staged team process theory, a moderated mediation model was established in which the competition-oriented culture is the mediating variable and the team efficacy is the moderating variable. 220 team leaders were surveyed, and the hierarchical regression analysis method was used to test the conceptual model. Results reveal that: (1) Team leaders’ promotion focus has significant positive influence on exploratory innovation and exploitative innovation. (2) Competition-oriented culture mediates the relationship between team leaders’ promotion focus and exploratory innovation, exploitative innovation. (3) Team efficacy positively moderates the relationship between competition-oriented culture, exploratory innovation and exploitative innovation, and positively moderates the mediating effect of competition-oriented culture.