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A spectrally efficient frequency division multiplexing (SEFDM) modulation has been proposed to improve system spectral efficiency, particularly for bandwidth-limited visible-light communication (VLC) systems. It employs non-orthogonal subcarriers to achieve bandwidth savings at the expense of serious intercarrier interference (ICI); thus, complicated detectors are required at the receiver to extract signals from the ICI. In this paper, we carry out an analysis of SEFDM modulation and establish a quasi-multiple-input multiple-output (MIMO) model for SEFDM-based systems. Based on this quasi-MIMO system model, for the first time, we propose to use an MMSE-sorted QR decomposition (MMSE-SQRD)-algorithm-based MIMO decoder to efficiently eliminate the ICI in a high-speed SEFDM-based wavelength-division multiplexing (WDM) VLC system. Using the MMSE-SQRD decoder, the WDM VLC system at an aggregate data rate of 2.4 Gb/s is experimentally demonstrated over a 2-m indoor free-space transmission, and up to 20% of bandwidth savings is achieved compared with that of the orthogonal frequency-division multiplexing (OFDM). The results clearly validate the effectiveness of the proposed MMSE-SQRD detector for SEFDM-based spectrum-compressed VLC system.