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Ground penetrating radar (GPR) forward simulation is an important part for accurate characterization of geological structures. Compared to standard second-order finite differences, higher-order finite differences and pseudo-spectral methods Maxwell solvers are able to reduce discretization effects (e.g. numerical dispersion). In this study, we innovatively present a general analytical approach of the arbitrary high-order pseudo-spectral Maxwell solver with perfectly matched layers (PMLs). It’s not only can avoid generating spurious signals that may affect the overall computational results through truncate the computational domain, but also have the advantageous parallel scalability of standard finite-different time-domain methods. The results show that the method can trade-off the flexibility of finite difference and maintain the accuracy of the pseudo-spectral method.