Summary: An HIV-1 epidemic model with time delay and saturation incidence rate is proposed. The global stability of a disease-free equilibrium \(E_0 (T_0, 0, 0)\) and a positive equilibrium \(E_+ (T^*, I^*, V^*)\) are discussed. By constructing Lyapunov functions and using LaSalle’s invariance principle, it is shown that if \(d\mu > s\gamma\beta\), the disease-free equilibrium \(E_0 (T_0, 0, 0)\) is globally asymptotically stable, and if \(d\mu < s\gamma\beta\), the positive equilibrium \(E_+ (T^*, I^*, V^*)\) is globally asymptotically stable, for all \(\tau \geq0\). Numerical simulations are carried out to illustrate the theoretical results.