High-speed multi-user access with high spectral efficiency is one of the key challenges for band-limited visible light communication (VLC) systems. In this paper, we propose a novel scheme for effective multiple-access VLC systems based on multi-band, Nyquist-filtered pulse amplitude modulation (PAM)-8 modulation. Within this scenario, the spectral efficiency can be improved from 1.5 to 2.73 b/s/Hz by implementing an appropriate Nyquist filter to suppress spectral bandwidth. We experimentally demonstrate a multi-band VLC system at 1.2 Gb/s after 1 m indoor free space transmission. The system performances have also been thoroughly investigated for different sub-band numbers, utilizing a rectangular filter in the frequency domain and a Nyquist filter based on square root raised cosine. The results show that the Nyquist-filtered PAM-8 signal can outperform a rectangular filtered signal. The maximum improvement of system capacity is up to 1.67 times for the Nyquist-filtered multi-band system. The results clearly show the advantage and feasibility of multi-band Nyquist PAM for high-speed multiple-access VLC systems.