Abstract: A simple SI epidemic model with age of vaccination is discussed in this paper. Both varing birth rate,the mortality rate caused by disease and vaccine waning rate are considered in this model.We prove that the global dynamics is completely determined by the basic reproductive number R(Ψ)(Ψdenotes per capita vaccination rate).If R(0)＜1, the disease-free equilibrium is a global attractor;If R(Ψ)＜1,the disease-free equilibrium is locally asymptotically stable;If R(Ψ)＞1,an unique endemic equilibrium exists and is locally asymptotically stable under certain condition. 

Key words: SI model, vaccination, equilibrium, stability