A SEIR infectious disease model with saturated incidence and latency is studied. The basic number of regeneration that determines extinction or persistence of diseases is determined. The existence of the model‘s equilibrium point is analyzed. Firstly, the global stability of disease-free equilibrium point is proved by constructing the Lyapunov function appropriately. Then, the asymptotic stability of local diseases-equilibrium point is analyzed by using the composite matrix judgment theorem. Finally, the global stability of local diseases-equilibrium point is proved by applying the competition system theorem.