The electromagnetic wave propagation problem of multilayer arbitrary dispersion periodic model was solved by using auxiliary differential equation-finite-difference time-domain (ADE-FDTD) method. The complex-conjugate pole-residue pairs were utilized to fit the parameters of any dispersive medium, and the model’s dielectric constant was expressed as a formula. Furthermore, the ADE was introduced into the FDTD iteration to deduce a general formula applied on the muti-layer arbitrary dispersion model. In addition, the electromagnetic characteristic simulation of Debye, Drude and solar cell structure were respectively solved. Simulation results show that the numerical calculation results are basically consistent with the CST commercial software simulation results, which proves the validity and universality of our method.