A highly-accurate numerical method is used to solve the two-dimensional Maxwell′s equations, where a computational fluid dynamics(CFD) based discontinuous galerkin(DG) method is employed for the spatial discretization and the four-step Runge-Kutta is used for time-stepping. In order to improve the efficiency, the quadrature-free implementation and the parallel computing based on mesh partitioning are used. Numerical tests indicate that highly-accurate solutions can be obtained when using high orders even on very coarse grids. More importantly, this CFD-based high-order DG method for the Maxwell′s equations is very suitable for complex geometries since it is implemented on unstructured mesh.