Non-orthogonal multiple access (NOMA) is an emerging multiple access technique and enjoys the benefits by enabling multiple users to multiplex in power domain. More recently, NOMA has been discussed in visible light communications (VLC) but less in underwater wireless optical communications (UWOC). In this paper, we evaluate the average channel capacity and outage probability of NOMA UWOC systems in the presence of turbulence. We consider the impacts of power or bandwidth allocation coefficient and oceanic turbulence fading coefficient on the performance of the designed system. Numerical results suggest that NOMA has higher data rate while orthogonal multiple access (OMA) such as orthogonal frequency division multiple access (OFDMA) has better coverage performance. As expected, turbulence degrades both the capacity and coverage performance.