High-speed visible light communication (VLC), as a cutting-edge supplementary solution in 6G to traditional radio-frequency communication, is expected to address the tension between continuously increased demand of capacity and currently limited supply of radio-frequency spectrum resource. The main driver behind the high-speed VLC is the presence of light emitting diode (LED) which not only offers energy-efficient lighting, but also provides a cost-efficient alternative to the VLC transmitter with superior modulation potential. Particularly, the InGaN/GaN LED grown on Si substrate is a promising VLC transmitter to simultaneously realize effective communication and illumination by virtue of beyond 10-Gbps communication capacity and Watt-level output optical power. In previous parameter optimization of Si-substrate LED, the superlattice interlayer (SL), especially its period number, is reported to be the key factor to improve the lighting performance by enhancing the wall-plug efficiency, but few efforts were made to investigate the influence of SLs on VLC performance. Therefore, to optimize the VLC performance of Si-substrate LEDs, we for the first time investigated the impact of the SL period number on VLC system through experiments and theoretical derivation. The results show that more SL period number is related to higher signal-to-noise ratio (SNR) via improving the wall-plug efficiency. In addition, by using Levin-Campello bit and power loading technology, we achieved a record-breaking data rate of 3.37 Gbps over 1.2-m free-space VLC link under given optimal SL period number, which, to the best of our knowledge, is the highest data rate for a Si-substrate LED-based VLC system.