The analysis of electromagnetic scattering and propagation in dispersive media is complicated in time domain，because its dielectric property is frequency-dependent. A disadvantage of the prevailing algorithms is the need to deduce different formulations for each dispersion model. In this paper，the shift operator finite difference time domain (SO-FDTD) method is developed. First，we prove that the complex permittivity of three kinds of general dispersive media models，i.e. Debye model，the Lorentz model and the Drude model, may be described by rational polynomial functions in jω. By introducing a shift operator zt，the constitutive relation between D and E is derived in discretised time domain. The shift operator method is then applied to the general dispersive medium case. The recursive formulation for D and E available for FDTD computation is obtained. Finally，the scatterings by a dispersive sphere and a PEC object covered with dispersive media are computed. The computed results are in good agreement with the literature and the one obtained by Mies series solution. This illustrates the generality and the feasibility of the presented scheme.