Abstract: This paper presents a novel method to simulate the electromagnetic scattering with Debye dispersion medium, which combines the alternative direction implicit-FDTD (ADI-FDTD) with auxiliary differential equations (ADEs). The ADI technology here adopts the split field equations, just as field in the perfectly matched layers (PML), which can lead the incident wave on the adjacent boundaries easily. Moreover, the update equations of electric and magnetic field components in this method are derived to the Debye medium. Finally examples are described to exhibit the high efficiency and accuracy of the proposed method compared with conventional FDTD.