This paper proposed a mixed time and frequency domain approximation algorithm that approximates a high order FIR filter using an IIR filter with lower order. The high order FIR filter is first shortened by an eigenfilter based time domain equalizer. The equalization residue is approximated in the spectral domain using, for example, the minimax criteria, such that the two approximation filters will join together to form the resulting IIR filter. The mixed time and frequency design criteria is based on the observation that both time and frequency domain property are important and inherently inefficient when used alone. Design examples have shown that the proposed design method can obtain very good approximation in both the impulse response and spectral response of the given filter which cannot be obtained by other design techniques.