In this paper, an improved complex-envelope alternating-direction-implicit finite-difference time-domain (CE-ADI-FDTD) method has been presented for the analysis of photonic-bandgap cavities. The improvement relies on a different approach of the perfectly matched-layer absorbing-boundary condition in order to avoid the formation of instability, as reported in the literature. The high numerical precision and efficiency obtained are clearly demonstrated through the agreement of the results obtained using CE-ADI-FDTD and their counterparts obtained using other rigorous approaches reported in the literature