In this study analytically systems of nonlinear ordinary differential equations such as modeling the pollution of a system of lakes are studied by a powerful analytical method that is called Reconstruction of Variational Iteration Method (RVIM). The RVIM technique provides us a simple way to ensure the convergence of solution series, so that we can always get accurate enough approximations. Also, it is independent of any small parameters at all. The method is capable of reducing the size of calculation and easily overcomes the difficulty of the perturbation technique or Adomian polynomials. The results are compared with the results obtained by MATLAB. Some plots are presented to show the reliability and simplicity of the methods.