In this article, homotopy perturbation method is implemented to give approximate and analytical solutions of nonlinear ordinary differential equation systems such as human T-cell lymphotropic virus I (HTLV-I) infection of CD4+ T-cells model. The proposed scheme is based on homotopy perturbation method (HPM), Laplace transform and Pade approximants. The results to get the homotopy perturbation method (HPM) is applied Pade approximants. Our proposed approach showed results to analytical solutions of nonlinear ordinary differential equation systems. Some plots are presented to show the reliability and simplicity of the methods.