Human immunodeficiency virus (HIV) has had an insightful impact about the state of healthiness of human immune system.Due to great improvement in drug therapy,HIV infections have been reduced by 17％ over the past eight years.It has been proved that most effective treatment HAART (Highly Active Anti Retroviral Therapy) mainly controls the diseases progression but it does not eradicate the diseases completely.Reverse Transcriptase Inhibitor drugs specially aesociated with virus specific Cytotoxic T-Lymphocyte (CTL) that declines with disease progression.CTL responses against AIDS pathogenesis could be potential in the dynamics of virus replication,recognition and clearance of infected cells.In this research article a mathematical model has been proposed on the basis of CTL response suppression in the chronic phase of infection due to presence of virus.We also consider the growth of the virus population from the infected CD4+T cells budding process and from the other infected cells like macrophages and thymocytes.Our analytical and numerical studies are consistent with existing observations from allied areas.