An improved shift operator finite-difference time-domain （SO-FDTD） method for general dispersive medium based on the implementation of infinite impulse response filter in digital signal processing technique is presented. Compared with the commonly used SO-FDTD, the storage variables in the improved SO-FDTD are reduced by 33% and computational efficiency is also increased. Finally, the generality and the feasibility of the presented scheme are validated by calculations of scattering by first order and second order dispersive objects.