We experimentally demonstrated a high-speed multi-user green and blue laser diode based underwater optical wireless communication (UOWC) system using non-orthogonal multiple access (NOMA) with polarization multiplexing. The system affords eight users with a record sum rate of 18.75 Gbps over 2-m underwater plus 0.5-m free-space channel. The modulation bandwidths of four detachable optical paths with different wavelengths and polarization states all exceed 1.5 GHz. The results suggest that the flexible balance according to both user fairness and overall throughput/sum rate can be achieved via an appropriate power allocation strategy. The joint optimization of driving current and user assignment ensures the feasibility of providing stable high-speed UOWC for multiple users. With the proposed OFDMA-NOMA scheme, user scale expands by twice while the sum rate for single path reaches 3.2 Gbps. Finally, the BER performances of NOMA modality in turbulent underwater environment with air bubbles of different flow rates are also discussed in detail.