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The staggered-grid Fourier pseudospectral time domain (PSTD) methods have proved to be efficient and accurate in seismic modeling, but less efforts have been extended to electromagnetic wave. In this paper, we apply the staggered-grid Fourier PSTD method in the simulation of three-dimensional electromagnetic wavefields in dispersive soils. The soil is considered as an M-th order Debye medium with additional static conductivity and a complex frequency shift perfectly matched layer (CFS-PML) is also presented to absorb the spurious reflections caused by truncated boundaries. In order to accelerate the simulation, we port the algorithm to GPU based on CUFFT, by which we need not to care much about the allocation and mapping of the global memory to the shared one in thread blocks. With GPU's inner data parallelism, we illustrate the efficacy of GPU in accelerating the simulation by achieving magnitude of speedup at no extra cost. We also validate the effect of CFS-PML and our approach to simulate the dispersive Debye medium.