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In this paper, a delayed human immunodeficiency virus (HIV)-1 infection model with absorption and cytotoxic T lymphocytes (CTL) immune response is studied. By using suitable Lyapunov functionals and LaSalle's invariance principle, it is proved that if the basic reproductive ratio is less than unity, the infection-free equilibrium is globally asymptotically stable; if the immune response reproductive ratio is less than unity and the basic reproductive ratio is greater than unity, sufficient conditions are derived for the global stability of the CTL-inactivated infection equilibrium; if the immune response reproductive ratio is greater than unity, sufficient conditions are obtained for the global stability of the CTL-activated infection equilibrium. Numerical simulations are carried out to illustrate the theoretical results. [ABSTRACT FROM PUBLISHER]