Abstract: The problem of control of a nonlinear singular system that is non-minimum phase is discussed. The state space of a nonlinear singular system is derived by an algorithm. Then, a synthetic output function is reconstructed, which is statically equivalent to the original one and allowing the arbitrary assignment of the zero dynamics of the state-space realization so as to enable the state space to be in minimum phase. And the state feedback is put into effect for the minimum phase system thus obtained to realize the state feedback for nonlinear singular system. The proposed method was applied to the SIR epidemic model with Logistic growth control problem for the purpose of eradicating the epidemic. Simulation results showed the validity and effectiveness of this method.