A non-orthogonal multiple access (NOMA) power allocation scheme on the basis of the sparrow search algorithm (SSA) is proposed in this work. Specifically, the logarithmic utility function is utilized to address the potential fairness issue that may arise from the maximum sum-rate based objective function and the optical power constraints are set considering the non-negativity of the transmit signal, the requirement of the human eyes safety and all users’ quality of service (QoS). Then, the SSA is utilized to solve this optimization problem. Moreover, to demonstrate the superiority of the proposed strategy, it is compared with the fixed power allocation (FPA) and the gain ratio power allocation (GRPA) schemes. Results show that regardless of the number of users considered, the sum-rate achieved by SSA consistently outperforms that of FPA and GRPA schemes. Specifically, compared to FPA and GRPA schemes, the sum-rate obtained by SSA is increased by 40.45% and 53.44% when the number of users is 7, respectively. The proposed SSA also has better performance in terms of user fairness. This work will benefit the design and development of the NOMA-visible light communication (VLC) systems.