Abstract: Compared with the body of revolution cylinder, the finite-difference time-domain (FDTD) algorithm for asymmetric cylinders corresponds to a periodic cyclic structure accumulated by different fan-shaped segments, which requires the azimuthal difference discretization processing of electric/magnetic field quantities and connected electric/magnetic currents. Meanwhile, mathematical singularities make it necessary to focus on the calculation of electric/magnetic field quantities on the axis. To reduce numerical dispersion errors, firstly, starting from the basic time-domain equations of the FDTD algorithm, the periodic cycle idea is used to process the azimuthal difference discretization of FDTD electric/magnetic field equations and Huygens volume electric/magnetic currents respectively. Secondly, taking whether overflow occurs in the FDTD electric/magnetic field difference discretization solution process as the judgment criterion, if the denominator of an electric/magnetic field equation contains a zero radial grid point during this process, separate on-axis processing is required for this electric/magnetic field equation. Then, Stokes′ theorem is used to derive the electric/magnetic field equations to be processed on-axis. Examples including scatterers with Mur boundaries, matched layers, electromagnetic band gaps and negative-refraction perfect lenses prove that the azimuthal and on-axis processing can effectively reduce the numerical dispersion errors of the FDTD algorithm for asymmetric cylinders and have no obvious influence on computational efficiency.