The public health issues have a lot of importance in our society, particularly the Human Immunodeficiency Virus (HIV) infection. Many models based on ordinary differential equations (ODEs) or partial differential equations (PDEs) have explained different aspects of the dynamics of the virus-immune system interaction. Although, they assume that various populations of cells and viruses have been homogeneously distributed over the space and time in which the infection takes place. In this paper, we present a cellular automaton (CA) that models the interaction between the cytotoxic T lymphocytes (CTLs) Cells and the immunoglobulin of the immune system and HIV in blood stream. Our approach is based on simple calculation rules that are easy to implement. The results of our (CA), taking into account the role of the two components of the adaptive immune system to overcome HIV infection reproduces the acute stage and the beginning of the second phase of the HIV infection development.