AbstractFDTD method plays an important role for simulation of different structures in various fields of engineering, such as RF/microwaves, photonics and VLSI. However, due to the CFL stability constraint, the FDTD time step is still small and the related CPU time is still large for modelling fine geometry where small cell sizes are required to resolve fields. As a result, the unconditionally stable CFL‐condition‐free ADI‐FDTD method is becoming a popular alternative to the FDTD method. The ADI‐FDTD method allows the use of larger time steps; however, it comes at the cost of larger errors. To mitigate the problem of these larger errors, in this paper we propose to modify the conventional ADI‐FDTD algorithm. The modifications are based on the fact that because the ADI‐FDTD is a truncated form of the Crank–Nicolson (CN) method, the truncated terms can be re‐introduced approximately into the ADI algorithms to improve accuracy. Two accuracy‐improved ADI‐FDTD algorithms are derived and then validated for two‐dimensional cases. Unfortunately, in the three‐dimensional case the proposed methods are not found to be unconditionally stable. Copyright © 2006 John Wiley & Sons, Ltd.