A novel finite-difference time-domain （FDTD） method combined with the semi-analytical recursive convolution （SARC） algorithm in DSP techniques for the analysis of electromagnetic characteristics in dispersive media is presented. In this method, the flexibility of FDTD in dealing with complicated objects is retained, while the advantages of absolute stability, high accuracy, low storage and high effectiveness of SARC in treating the linear system problem is introduced. The proposed SARC FDTD approach can therefore be applied to the analysis of general dispersive media provided the poles and corresponding coefficients in the dispersive medium model of interest are given. Three typical kinds of dispersive model, i.e. Debye, Drude and Lorentz medium are tested to demonstrate the feasibility of the present scheme.