The paper presents a SEIRS epidemic model with non-monotone incidence rate and time delay describing a latent period.By analyzing the corresponding characteristic equations,the local stability of a disease-free equilibrium and an endemic equilibrium was established.When the basic reproduction number R₀≤1,the global stability of the disease-free equilibrium was proved.When the basic reproduction number R₀>1,by means of Lyapunov functional,sufficient conditions were obtained for the global asymptotic stability of the endemic equilibrium.Computer simulations were carried out to illustrate the main theory.