Scientific computation plays an important role in natural sciences, engineering and technology. It has become an indispensable tool in many areas. The Poisson equation is an essential partial differential equation in fluid dynamics and electromagnetic. Due to its analytical solution of a Poisson equation is difficult to obtain, an alternative method is to find its numerical solution. A classical method to get the numerical solution of the Poisson equation is the standard five-point or nine-point difference scheme, which is simple to use and secondorder accurate. In order to enhance the accuracy of the difference scheme, it is often required to have finer mesh split or to use more complex difference scheme, which will result in much more computing time and larger amount of data storage.