In this paper, we for the first time propose and investigate a novel discrete Fourier transform-spread-orthogonal frequency division multiplexing with quadrature index modulation (DFT-S-OFDM-QIM) scheme for practical visible light communication (VLC) systems. By performing subcarrier index modulation on both the in-phase and quadrature components of each subcarrier, OFDM-QIM achieves a higher spectral efficiency than conventional OFDM with index modulation (OFDM-IM). Moreover, the peak-to-average power ratio (PAPR) of OFDM-QIM can be substantially reduced by applying DFT spreading, and hence DFT-S-OFDM-QIM exhibits high tolerance against light-emitting diode (LED) nonlinearity. The superiority of the proposed DFT-S-OFDM-QIM scheme over other benchmark schemes has been successfully verified by both simulation and experimental results.