In this work, the unconditional stability of the ADI-FDTD method in lossy media has been proven in our approach. The numerical dispersion and stability characteristics of the ADI- FDTD method in lossy media are analyzed. The dispersion analysis actually has a more general meaning, which includes the investigations of both the numerical loss and numerical dispersion, since the propagation constant is complex for the lossy media case. This is different from the previous dispersion analysis based on the assumption of lossless media, where the propagation constant is purely imaginary. So it is necessary to perform the dispersion analysis for the ADI-FDTD method in lossy media to reveal its individual characteristics, which will be meaningful for the application and further development of the ADI-FDTD method in lossy media.