In the traditional differential equation solution, the multi-region spectral method only constructs the approximation scheme of the equation independently in the local element, and different elements exchange information by penalizing the boundary or the numerical flow function on the boundary, which has good flexibility and high precision in the selection of the basis function and the generation of the grid. In this paper, the numerical solution of Maxwell Differential Equation is studied based on multi-region spectral method. In order to further reduce the computational cost of solving the equation, various difference numerical flux formats are introduced. By use of the upwind flux, the scale of the hybrid model supported by the format is reduced. The non-physical eigenvalues cannot be removed and the spectra are clearly separated, which makes it possible to separate the physical mode from the mixed mode. The algorithm is suitable for arbitrary mesh generation with high precision and high efficiency, and the effectiveness of the algorithm is verified by numerical examples.