We performed a two-dimensional full band, ensemble Monte Carlo simulation of a GaN metal-semiconductor field effect transistor (MESFET). The substrate is the wurtzite n-GaN with a background doping density 3×1017cm-3 and 0, 1 μm thick. The doping concentration of both source and drain is 2×1019cm-3. Au is assumed for the gate material. The Schottky contacts are formed between Au and wurtzite GaN. The Schottky barrier height of Au/GaN is assumed to be 0.98eV. The gate is 0.1μm length, and the space between source and drain is 0.4μm. The characteristics of the drain current Id versus drain-source voltage VDS for gate-source voltages varying from 0-6V in IV step is obtained by Monte Carlo simulations. At VDS=15V and VGS=0V, The drain current Id is 5.03A/cm, which is higher value. The transconductance Gm versus VGs characteristics are also analyzed by Monte Carlo simulations. The Gm-VGS curve is bell shaped and the maximum Gm is 112 ms/mm at VDS=15V and VGS=1.5V. The current gain cutoff frequency fT is 98 GHz at VDS=15 V and VGS=0V.