A new method for approximate analytic series solution called multistep Laplace Adomian Decomposition Method (MLADM) has been proposed for solving the model for HIV infection of CD4(+) T cells. The proposed method is modification of the classical Laplace Adomian Decomposition Method (LADM) with multistep approach. Fourth-order Runge-Kutta method (RK4) is used to evaluate the effectiveness of the proposed algorithm. When we do not know the exact solution of a given problem, generally we use the RK4 method for comparison since it is widely used and accepted. Comparison of the results with RK4 method is confirmed that MLADM performs with very high accuracy. Results show that MLADM is a very promising method for obtaining approximate solutions to the model for HIV infection of CD4(+) T cells. Some plots and tables are presented to show the reliability and simplicity of the methods. All computations have been made with the aid of a computer code written in Mathematica 7.