Team has been widely applied in various fields, in which the collaboration efficiency of a team is the main consideration under the constraints of skill requirements. In educational scenarios, an educational institution usually builds a team of students with different skills to attend a competition, in which team communication cost and team benefit are two main concerns. Nevertheless, both educational fairness and student conflicts should be taken into account when forming a team for a competition. Furthermore, in forming a team for a competition, a successful team should be robust to avoid the risk of team members' departure. This paper aims to form a robust team for a competition taking into account educational fairness and student conflicts. Firstly, the authors establish a team formation model for a competition in which robustness, educational fairness, and student conflicts are simultaneously considered. In the model, we formalize a robust team formation problem, in which team robustness and student conflicts are described as constraints, and team communication cost, team skill-benefit and the team fairness are handled as the objective function. The higher the objective function value, the better the team formed. Secondly, we design a genetic algorithm with partial repair operators (PR-GA for short) to form a robust team, in which the parameter repair probability determines the probability of changing an infeasible solution to a feasible one. Finally, we conduct extensive experiments to evaluate the performance of our algorithm. We investigate the impact of repair probability on the formed team. The results show that with an increase in the repair probability, the objective function value of the formed team arises with the cost of increasing the running time of the algorithm. In addition, for a given set of students, the objective function value and the size of the team formed by all algorithms increase with increasing robustness parameter. In addition, for a given set of students, the running time of all algorithms increases with the increase of the robustness parameter. Although slightly worse than AR-GA (a genetic algorithm that repairs all infeasible solutions) in terms of objective function value, our proposed PR-GA consumes less running time for all instances. In general, our PR-GA has a shorter running time with a 22.3% decrease compared to AR-GA. Moreover, our PR-GA holds the second best in terms of team size and convergence speed.