An upwind scheme for periodic electromagnetic field problems in moving media is developed in the paper. When the Peclet number of discrete grid is larger than one, the procedure using Galerkin method will provide spurious oscillations in the computed results. To suppress these oscillations, an upwingd finite element method with two different upwind parameters in upwind and downwind sides is introduced. To one dimensional problems, this method can provide nodally exact solution for even spacing grids. Based on the one dimensional result, a cooresponding two dimensional scheme is suggested and tested by a 2-D model.