AbstractThis article proposes a new unconditionally stable explicit finite‐difference time‐domain (FDTD) scheme for 3D Maxwell equation.The proposed scheme is based on alternating‐direction explicit method and Crank–Nicolson (CN)‐based FDTD method, and we present two versions of the proposed method. Numerical stability and dispersion analysis of the new algorithm were also presented. The results by the proposed method are compared with the results by the conventional FDTD method, alternating‐direction implicit method, and CN‐based FDTD method. As a result, it is confirmed that the proposed method is unconditionally stable and the efficiency is superior to the conventional method if the minimum cell size in the computational domains is required to be much smaller than the wavelength. © 2012 Wiley Periodicals, Inc. Microwave Opt Technol Lett 54:1269–1273, 2012; View this article online at wileyonlinelibrary.com. DOI 10.1002/mop.26802