In this paper, a five–dimensional mathematical model is proposed for the transmission dynamics of HIV/AIDS within a population of varying size. In writing the model, we have divided the population under consideration into five sub classes of susceptible, infective, pre-AIDS, AIDS related complex and that of AIDS patients. The model has two non- negative equilibria namely, a disease free and the endemic equilibrium. The model has been studied using stability theory. It is shown that the positive non-trivial equilibrium is always locally stable but it may become globally stable under certain condition showing that the disease becomes endemic due to constant migration of the population into the habitat. The effect of various parameters on the spread of the disease has also been discussed.