Background <p>The complex constraints contained in the cooperative guidance problem for the multi-missiles attacking maneuvering target result in the challenge of the cooperative guidance law design.</p> Purpose <p>In this paper, the cooperative guidance law is designed by using the Zu-Chongzhi-type symplectic method that can be used to avoid the constraint default problem efficiently.</p> Methods <p>Firstly, the considered cooperative guidance problem is modeled by a differential system with complex multi-constraints. Then, the complex algebraic-integral-differential equality-inequality constraints are combined as an equality constraint. Finally, the Zu-Chongzhi-type symplectic method is employed to solve the ordinary differential system with the combined equality constraint to design the cooperative guidance law for the considered cooperative guidance problem.</p> Results <p>From the numerical results, it can be found that, comparing with the proportional guidance law and the sliding mode guidance law, the Zu-Chongzhi-type symplectic method can be used to design the cooperative guidance law more effectively. In addition, the difference between the cooperative guidance laws of two cases are also presented in the numerical results.</p> Conclusions <p>The main contribution of this paper is providing a new approach to design the cooperative guidance law of the cooperative guidance problem that can satisfy the complex algebraic-integral-differential equality-inequality constraints perfectly.</p>