In this talk,we formulate an HIV latent infection model with spatial diffusion and delays is derived and investigated. Applying the definition of the next reproduction operator, we obtain the basic reproduction number R_0, which is a threshold value for determining whether the breakout of HIV infection or not. More precisely, the infection-free equilibrium is globally attractive if R_0<1 and the infection is uniformly persistent if R_0>1. The influences of time delays, HAART treatment and infection heterogeneity on HIV infections are discussed via numerical simulations. This work reveals that the use of the spatially averaged parameters may underestimate HIV infection. Therefore, the spatial heterogeneity is a key factor that cannot be ignored when clinical medical staff design the treatment strategies for HIV infection.