A HIV-1 model with two distributed intracellular delays and general incidence function is studied. Conditions are given under which the system exhibits the threshold behavior: the disease-free equilibrium E0 is globally asymptotically stable if R0≤1; if R0>1, then the unique endemic equilibrium E1 is globally asymptotically stable. Finally, it is shown that the given conditions are satisfied by several common forms of the incidence functions.