As the interception probability and interception efficiency of anti-missile system consistently increased, the probability for a single ballistic missile breaking the anti-missile system to achieve the attack task is gradually decreasing, thereafter comes the strategy multi-ballistic missile cooperative attack. The cooperative attack of multi-ballistic missile during the free flight segment is easy to achieve, with the missile called warhead at this stage. To solve the problem of modeling and output consensus of cooperative attack for multiple warheads(hereinafter referred to as multi-warhead)in the free-flight segment of ballistic missile, a three-dimension nonlinear state space model for multi-warhead space motion in the free-flight segment is established. On this basis, the characteristic of the model and the challenges brought by the nonlinear dynamic of the model to the cooperative attack of multi-warhead receives detailed analysis. To deal with the above challenges and realize the output consensus of the cooperative attack architecture for leader-followers multi-warhead, a kind of cooperative acceleration command signal is designed for the followers by using the input-output feedback linearization control theory, and the effectiveness of the designed command signal is verified by detailed numerical simulation. The result of simulation shows that the output consensus of cooperative attack architecture for leader-followers multi-warhead is realized under the given performance requirement on all axes of the leader's launch coordinate system. The faster the velocity of leader varies and the larger the real part modulus value of convergence coefficient is, the faster the convergence speed of velocity tracking error and the smaller the velocity tracking error will be. Finally, the performance of the output consensus will be even better.