Abstarct: We present a delay-differential equation model with optimal control that describes the interactions between human immunodefciency virus (HIV ), CD4 +T cells, and cell-mediated immune response. Both the treatment and the intracellular delay are incorporated into the model in order to improve therapies to cure HIV infection. The optimal controls represent the efciency of drug treatment in inhibiting viral production and preventing new infections. Existence for the optimal control pair is established, Pontryagin’s maximum principle is used to characterize these optimal controls, and the optimality system is derived. For the numerical simulation, we propose a new algorithm baxsed on the forward and backward difference approximation.