In this paper the current-voltage characteristics of a submicron GaAs MESFET is simulated by using the self-consistent ensemble Monte Carlo method. The numerical algorithm employed in solving the two-dimensional Poisson equation is the successive over-relaxation(SOR) method. The total number of employed superparticles is about 1000 and the field adjusting time is 10fs. To obtain the steady-state results the simulation is performed for 10ps at each bias condition. The simulation results show the average electron velocity is modified by the gate voltage.