It is a well-documented phenomenon that a group's gender composition can impact group performance. Understanding why and how this phenomenon happens is a prominent puzzle in the literature. To shed light on this puzzle, we propose and experimentally test one novel theory: through the salience of gender stereotype, a group's gender composition affects a person's willingness to lead a group, thereby impacting the group's overall performance. By randomly assigning people to groups with varying gender compositions, we find that women in mixed-gender groups are twice as likely as women in single-gender groups to suffer from the gender stereotype effect, by shying away from leadership in areas that are gender-incongruent. Further, we provide evidence that the gender stereotype effect persists even for women in single-gender groups. Importantly, however, we find that public feedback about a capable woman's performance significantly increases her willingness to lead. This result holds even in male-stereotyped environments.