In this investigation, attempts have been made to solve two-dimension nonlinear viscous flow between slowly expanding or contracting walls with weak permeability by utilizing a semi analytical Akbari Ganji's Method (AGM). As regard to previous papers, solving of nonlinear equations is difficult and the results are not accurate. This new approach is emerged after comparing the achieved solutions with numerical method and exact solution. Based on the comparison between AGM and numerical methods, AGM can be successfully applied for a broad range of nonlinear equations. Results illustrate, this method is efficient and has enough accuracy in comparison with other semi analytical and numerical methods. Ruge-Kutta numerical method, Variational Iteration Method (VIM), Homotopy Perturbation Method (HPM) and Adomian Decomposition Method (ADM) have been applied to make this comparison. Moreover results demonstrate that AGM could be applicable through other methods in nonlinear problems with high nonlinearity. Furthermore convergence problems for solving nonlinear equations by using AGM appear small.