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Motivated by previous work on modeling dispersive media with a single pole, Z-transform conductivity model, we present an absorbing boundary condition (ABC) for such media, based on the one-way wave equation. The applicability of the method is tested on a three dimensional (3-D) finite-difference time-domain grid excited with a broadband Gaussian pulse, modulated at 2 GHz. For such media and this high frequency range, the resulting reflection ratio for normal incidence is less than 1%. A comparison in 2-D grids with the original perfectly matched layer (PML) ABC for dispersive media shows that for small angles of incidence, this Mur-type ABC is superior. In addition, it requires no additional storage of field components, is easy to implement, and is readily parallelizable. Therefore, despite its limitations, it can be a good alternative to other PML-based ABCs for lossy dispersive media, in high frequency applications such as underground radar or microwave imaging.