Abstract: In view of the research on the improvement of water environment by ecological water diversion,a mathematical model of nutrient-toxin-producing phytoplankton under state impulse feedback control is constructed.Firstly,the boundedness,existence and stability of the boundary and positive equilibrium point of the uncontrolled system are investigated.The fact that there maight exist one,two or three positive equilibrium points in the system is pointed out,and the existence of saddle-node point is also proved.Then,the successor function,the Bendixson domain theorem and the contraction mapping principle of semi-continuous dynamical system theory are applied to investigate the existence,uniqueness and stability of order-1 periodic solution.Finally,the existence of order-1 periodic solution is verified by numerical simulation.