The HIV infection model of CD4+T cells corresponds to a class of nonlinear ordinary differential equation systems. In this study, we provide the approximate solution of this model by using orthonormal Bernstein polynomials (OBPs). By applying proposed method the nonlinear system of ordinary differential equations reduces to a nonlinear system of alge- braic equations which can be solved by using a suitable numerical method such as Newton’s method. We prove some useful theorems concerning the convergence and error estimate associated to the present method. Finally, we apply the proposed method to get the numerical solution of this model with the arbitrary initial conditions and values. Furthermore, the numer- ical results obtained by the suggested method are compared with results achieved by other previous methods. These results indicate this method is agreement with other previous methods.
