According to the specialty of infection transmission that infected individuals have different infectivities in different stages and that infected individuals can move from a stage into the other stage with the development of infection, an epidemic model with stage is established. The basic reproduction number is found by means of the next generation matrix. By applying the theory of asymptotically autonomous systems, the following results are obtained: the disease-free equilibrium is globally asymptotically stable when the basic reproduction number is not greater than 1; the endemic equilibrium is locally asymptotically stable when the basic reproduction number is greater than 1. When the disease is not fatal, the endemic equilibrium is globally asymptotically stable if it exists.