Random dopant fluctuation (RDF) in MOSFET has been an issue recently due to the scaling down of CMOS process. Impedance field method has mainly used as a solution to predict effects of RDF previously. In addition, a new model, which converts a Poisson's equation into a Green's function based form, estimates inhomogeneous term of differential equation through charge distribution. In this paper, a Green's function based 2-D MOSFET model is proposed. The model starts from the Poisson's equation to obtain the initial conditions and then sum of Green's function based formula and Laplace equation provide voltage distribution, charge distribution, and drive current as the modeling results. We also verify its effectiveness through the comparison with TCAD simulation results.