Abstract: A periodic impulsive food chain system of three species with functional response is investigated.The system is modeled by an impulsive differential equations with periodic coefficients.By using the Floquet theory and the comparison principle of impulsive differential system,as well as some analytical techniques,the dynamic behavior of the system is researched.We obtain the threshold conditions for the global asymptotic stability of the pest extinction periodic solution,and prove that the system is persistent when the threshold condition is not satisfied.