Abstract In this paper, we have investigated the dynamic behavior of an SEI model with acute and chronic stages. Firstly by using Theorem 4.1 of Busenberg and van den Driessche [S. Busenberg, P. van den Driessche, Analysis of a disease transmission model in a population with varying size, J. Math. Biol., 28 (1990), 257–270], we have shown that if the basic reproduction number R 0 > 1, the unique endemic equilibrium is global asymptotically stable. The results obtained here improved the main results of Yuan and Yang [J. Yuan, Z. Yang, Global dynamics of an SEI model with acute and chronic stages, J. Comput. Appl. Math. (2007), doi: 10.1016/j.cam.2007.01.042]. Then the criterion for robustness of the system is established under stochastic perturbations. Finally, numerical simulations are performed to illustrate the analytical results.