Based on reinfection, an epidemic model with vaccination, incubation and infection ages is presented to understand the impact of age of vaccination, age of latency and age of infection on global dynamics of the model. It is shown that the global dynamics of the model is determined by the basic regeneration number. First, the boundedness, existence, nonnegativity and asymptotic smoothness of the model are established by the theory of integrating partial differential equations along characteristic lines. Then, the steady states and basic reproduction number of the model are obtained by the theory of solutions to differential equations. By constructing a suitable Lyapunov functional and using the LaSalle invariance principle, it is verified that the disease-free steady state is globally asymptotically stable if the basic regeneration number is less than 1, and unstable if the basic regeneration number is larger than 1. Finally, by numerical simulation it is verified that the solution converges to the disease-free equilibrium point.