An attitude control method is proposed based on Eigenaxis rotation to satisfy the rapidity demands of kinetic kill vehicles, and realize rapid attitude tracking of target. Eigenaxis rotation is considered as an optimum maneuver mode since it can provide the shortest angular path for the attitude tracking. Based on error kinetic equation, the control algorithm achieves Eigenaxis rotation in the process of controlling attitude angles by introducing error quaternion and angular velocity. The globally stability of the algorithm is proved using Lyapunov function. Finally, mathematical simulation is conducted, which demonstrates that the algorithm can realize the shortest path of Eignaxis rotation with smooth maneuvering process and high precision.