The dispersive periodic structures are simulated by the split-field finite difference time domain (FDTD) method. According to the Floquet theorem, a set of auxiliary elements are introduced into the FDTD iteration to deal with electromagnetic simulation of oblique incidence on periodic structures, by combining the periodic and absorption boundary condition. We here extend the split-field method to the study of periodic dispersive structures by combining the Z transformation method. The iterative equations of the Drude dispersive model are also provided. By Comparing analytical and other numerical results, the efficiency and wide applicability of our method are demonstrated.