In this paper, the stability analysis of the Mur's first order absorbing boundary condition (ABC) in the alternating direction implicit finite-difference time-domain (ADI-FDTD) method is presented. To analysis the stability of this scheme, the amplification matrix is derived. The effect of wave propagation direction on the stability of this scheme is investigated. The numerical dispersion relation of this scheme is also derived analytically from the amplification matrix. From the theoretical stability analysis and numerical simulation, it is found that the Mur's first order ABC in the ADI-FDTD method will be unstable.