Abstract: A HIV-1 infection model with time delay and CTL immune response is studied. By analyzing the corresponding characteristic equation, the local stability of each of feasible equilibria and the existence of Hopf bifurcation are established, respectively. By constructing the appropriate Lyapunov function, the global stability of the infection-free equilibrium and the CTL-activated infection equilibrium are studied. Numerical simulations are carried out to illustrate the theoretical results.