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Construction of electromagnetic wave propagation model in layered pavement structure is a key problem for applying ground penetrating radar (GPR) to the road quality detection. A first-order explicit symplectic Euler method with Higdon absorbing boundary condition is presented to simulate GPR wave propagation in 2-D pavement structure. The incident wave is considered as line source and plane wave source, respectively. The total-field/scatter-field technique is used to simulate plane wave excitation. Numerical examples are provided to verify the accuracy and efficiency of the proposed algorithm. It can be observed that the symplectic Euler method achieves almost the same level of accuracy as the finite-difference time-domain scheme, while saving CPU time considerably.