This paper investigates the group formation control problem of second-order multi-agent systems from the viewpoint of aggregative game. One leader is selected from each group, and the game cost function is designed to realize the desired formation. An interesting discovery is that the Nash equilibrium of a quadratic aggregative game constitutes the desired formation of leaders. Moreover, a distributed algorithm is designed for these leaders to form the desired formation by seeking the Nash equilibrium, where every leader estimates the aggregate of the game. Furthermore, the convergence of the algorithm is analyzed via the Lyapunov stability theory. Compared with existing formation protocols, second-order agents using this algorithm converge to the desired formation without using neighbors positions and velocities information. The followers use a control protocol different from that of leaders, and by adjusting the positions and velocities relative to neighbors and leaders, the desired formation is formed. Finally, the above theoretical results are verified by numerical simulations.