Abstract: A kind of model concerning controlling plant root pests with impulsive state feedback control is analyzed. The global asymptotic stability of the positive equilibrium of the system without impulsive state feedback control is obtained by using the qualitative theory of ordinary differential equation, the existence and stability of order one periodic solution of the system with impulsive state feedback control have been studied by the geometry theory and the method of successor functions. The results show that the density of pest can be controlled to be lower than Economic Injury Level.