Abstract: The AC servo system of air-defense rocket launcher, which is a nonlinear dynamic system, can exhibit a variety of chaotic or limit-cycle phenomenon under some choices of system parameters and external inputs, and its chaotic characteristics are more prominent. Based on the mathematical model of the air-defense rocket launcher AC servo system, the property of equilibrium points was analyzed and the existence of Hopf bifurcation was proved. In addition, bifurcation diagram, Lyapunov exponent map and phase plane diagram were also given in this paper. An adaptive state-feedback controller was designed to control the chaotic movement to reach a stable status under certain system parameters. Numerical simulation proves the validity of this control method.