To reduce computational loads and save communication resources of cooperative multi-missile systems based on the event-triggered mechanism, the distributed differential game guidance laws are investigated. First, the cooperative multi-missile interception problem is converted into multi-player zero-sum differential games. The proposed guidance laws are derived by addressing the couple event-triggered-based Hamilton-Jacobi-Bellman equation, which is solved by using the adaptive dynamic programming technique. Meanwhile, adaptive weight tuning laws and event-triggered conditions are designed. The proposed guidance laws can guarantee the stability of the nonlinear multi-missile system, which is proved using the Lyapunov method. Then, the estimated weights of the neural network and consensus tracking errors are ensured to be uniformly ultimately bounded. Besides, a minimal inter-sample time is established for avoiding the Zeno behavior. Finally, some experiments are provided to illustrate the effectiveness of the proposed guidance laws. Compared with traditional distributed differential game guidance laws, the proposed guidance law reduces the number of state updates of the cooperative system controller by 65.36%. The computational burden and communication resources of the control system can be greatly reduced.