In this study, a mathematical model of Human Immunodeficiency Virus with a view of infection at window period is studied. The model was characterized through optimal control approach and it was established that minimum medications could be used to maximize uninfected CD4+T cells concentration, while the efficacy of drug therapy could be used to prevent the new cells from being infected in the human body system . Finally Gauss Siedel-like finite difference method was employed to carry out the numerical simulation using real life data to validate the reality of the model studied.