During the process of starting a business, in an entrepreneur team, there’s not only a collaborative relationship among team members, there’re also competitions between them. To avoid the consequence of team output reduction caused by the competitive behavior of team members to fight for rights and interests, it’s necessary to figure out the influence of the Competitive-Complementary Relations (CCR) among members on the performance of the team, so this paper aims to study the cultivation of teamwork quality of college students in entrepreneur team from the perspective of CCR. At first, relevant indexes were selected from four aspects of team factor, teacher factor, team member factor, and efficacy factor to form an Evaluation Index System (EIS) for assessing the teamwork quality of the college student entrepreneur team; then, this paper employed a combinatorial weighing method to integrate the weights obtained by the Entropy Weight Method (EWM) and the Variation Coefficient Method (VCM), constructed conceptual models for the competitive efficacy and complementary efficacy of the college student entrepreneur team, and introduced the methods for calculating the competitive degree index and complementary degree index of team members in detail. After that, the paper used a gray prediction model GM (1, 1) to predict the teamwork quality of several sample college student entrepreneur teams within the study period based on the completion degree of entrepreneurial tasks, and used a coupling model to analyze the coupling and coordination degree between competitive degree, complementary degree, and team performance. At last, experiment results proved the effectiveness of the proposed EIS and models.