A class of delayed HIV-1 infection models with latently infected cells was proposed. The basic reproductive number $ R_0 $ was defined, and the existence conditions of disease-free equilibrium $ P_0 (x_0 , \, 0, \, 0, \, 0) $ and chronic-infection equilibrium $ P^\ast (x^\ast , \, \omega ^\ast , \, y^\ast , \, v^\ast ) $ were given. First, the local asymptotic stability of infection-free equilibrium and chronic-infection equilibrium was obtained by the linearization method. Further, by constructing the corresponding Lyapunov functions and using LaSalle's invariant principle, it was proved that when the basic reproductive number $ R_0 $ was less than or equal to unity, the infection-free equilibrium $ P_0 (x_0 , \, 0, \, 0, \, 0) $ was globally asymptotically stable; moreover, when the basic reproductive number $ R_0 $ was greater than unity, the chronic-infective equilibrium $ P^\ast (x^\ast , \, \omega ^\ast , \, y^\ast , \, v^\ast ) $ was globally asymptotically stable, but the infection-free equilibrium $ P_0 (x_0 , \, 0, \, 0, \, 0) $ was unstable. The results showed that a latently infected delay and an intracellular delay did not affect the global stability of the model, and numerical simulations were carried out to illustrate the theoretical results.