This paper considers a mathematical model to study the effect of stem cell transplantation on HIV-1 patients. The model was recently proposed by the author. The viral dynamics is described by three ordinary differential equations covering three populations: uninfected T-cells, infected cells and free virus, but, stem cells lineage passes through many stages to become specialized T- cells. The stability of the equilibrium points has been previously analyzed locally. Here we study the global stability. The proposed analysis can help medicine make the right decision about the proposed therapy