The transmission data rate of visible light communication (VLC) systems is mainly limited by the modulation bandwidth of light-emitting diodes (LEDs). Pre-equalization (PE) techniques in combination with advanced modulation formats have been employed to enhance the data rate of LED-based VLC systems. In this paper, we experimentally demonstrated a high spectral-efficiency filter bank multi-carrier (FBMC) and non-orthogonal multiple access (NOMA)-based VLC transmission system using digital-to-analog converter-based PE (DAC-PE) and discrete Hartley transform (DHT) precoding technique. Two PE techniques, i.e., DAC-PE and digital pre-equalization (DPE), are comparatively investigated in both orthogonal frequency-division multiplexing (OFDM)-NOMA-based VLC systems and FBMC-NOMA-based VLC systems. The results exhibit that, with the help of DHT precoding, the DAC-PE scheme outperforms the DPE scheme at the optimal power ratios (PRs). Besides, the FBMC-NOMA scheme can provide better bit error rate (BER) performance and higher data rate than OFDM-NOMA. At the optimal PR of 6 dB, the FBMC-NOMA signal with a record net data rate of 3.84 Gbit/s after 2.3-m free-space link transmission can be achieved with the BER below 3.8 × 10−3.