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In this paper, we rigorously analyze an HIV-1 infection model with CTL immune response and three time delays which represent the latent period, virus production period and immune response delay, respectively. We begin this model with proving the positivity and bound-edness of the solution. For this model, the basic reproduction number R0 and the immune reproduction number R1 are identified. Moreover, we have shown that the model has three e-quilibria, namely the infection-free equilibrium E0, the infectious equilibrium without immune response E1 and the infectious equilibrium with immune response E2. By applying uctuation lemma and Lyapunov functionals, we have demonstrated that the global stability of E0 and E1 are only related to R0 and R1. The local stability of the third equilibrium is obtained under four situations. Further, we give the conditions for the existence of Hopf bifurcation. Finally, some numerical simulations are carried out for illustrating the theoretical results. [ABSTRACT FROM AUTHOR]