A finite impulse response (FIR) equalizer is practically employed in conjunction with the Viterbi detector for data detection process in magnetic recording channels. However, the FIR equalizer with a large number of taps is required at high density storage channels. It is well-known that an infinite impulse response (IIR) filter with a small number of taps can closely approximate such an FIR filter. In this paper, we present three methods of designing the IIR equalizer for magnetic recording channels. Results indicate that, when the number of equalizer taps is small (e.g., 3 taps) and the normalized recording density is high, the IIR equalizer designed based on the minimum mean-squared error approach performs much better than the FIR equalizer, especially in longitudinal recording channels.