We present computationally-efficient implementation techniques of multiple-input multiple-output (MIMO) frequency-domain equalization (FDE) that deals with a modal dispersion effect underlying in long-haul mode-division-multiplexed (MDM) signal transmission. Computational complexity reduction comes from twofold approaches: the first is out-of-band-exclusive (OBE) FDE for removing redundant computations in MIMO-FDE processing by taking a practical signal bandwidth occupation into account. A second appoarch, referred to as overlapping-reduced (OR) FDE, further reduces the complexity by modifying an overlapping ratio in the overlap-and-save FDE method to below 0.5. We show that OBE-FDE reduces complexity for processing with a larger number of spatial channels compared with the conventional FDE, and that the overlapping ratio is minimized up to 0.25 by the OR-FDE approach. Also shown is an experimental demonstration using the results of three-mode MDM transmission with different inter-mode coupling scenarios, verifying that the complexity is decreased by up to 37 % with negligible deterioration in signal performance by using the proposed method.