Abstract: For the case that the simulation target contains irregularly shaped patches, a weakly conditional stabilized finite-difference time-domain (FDTD) method based on auxiliary differential equations (ADE) is proposed in order to achieve more efficient and accurate calculations. Starting from the time-domain Maxwell's curl equations, the iterative formula for introducing the conformal technique in the weakly conditional stable FDTD method based on the ADE is derived and programmatically implemented, and the accuracy and stability of the proposed method has been verified. This method is applied to the simulation of a wideband polarization converter. The obtained results show that the stability conditions and memory occupation are unaffected, the polarization conversion rate is greater than 90% in the frequency band from 9.9 GHz to 16.6 GHz, and the relative bandwidth can reach 48.4%; compared with the weak conditional stabilization method and the conformal method in dispersive media, the proposed method improves the accuracy and computational efficiency of the calculations and meets the needs of practical engineering simulation. In addition, as a weak conditional stabilization method, it is suitable for simulating objects with fine structures in a single direction.