This paper describes a two-dimensional analysis of the potential distribution and electron concentration of the MODFET at channel using FDM. More exact analysis can be obtained by two-dimensional analysis which considers parasitic effects ignored in one-dimensional analysis. Using Poisson and Shrodinger equations, the potential distribution and the wave function are calculated within a constant error bound. As a result, the relations between the thickness of spacer, doping concentration of (n) AlGaAs layer, and the sheet density of the 2DEG (2 Dimensional Electron Gas) of MODFET at channel are suggested quantitively. The sheet density of the 2DEG is increased as the thickness of the spacer is decreased of the doping concentration of the (n)AlGaAs layer is lowered.