In order to overcome the limitation of narrow modulation bandwidth on the performance in the visible light communication (VLC) systems, non-orthogonal multiple access (NOMA) is applied to the downlink VLC networks in this paper to improve the sum rate performance effectively. We first propose an optimal power allocation strategy which is based on the multi-factor control (MFOPA), aiming to maximize the total system capacity subject to ensuring all users' quality of service (Qos) and fairness, as well as illumination requirements. The analytical results indicate that the proposed MFOPA could provide higher system sum rate and better user fairness as well as guarantee the Qos and eye safety of each user at the same time when compared with the static power allocation (SPA) and gain ratio power allocation (GRPA) schemes, especially in high demand for signal-to-interference-plus-noise ratio (SINR). What is more, considering the residual interference may exist during the successive interference cancellation (SIC) at the receiver, namely imperfect SIC, the interference cancellation factor is also taken into account in MFOPA strategy. The numerical results are shown to demonstrate the robustness and effectiveness of the MFOPA in NOMA-VLC when the residual interference remains. INDEX TERMS Visible light communication (VLC), non-orthogonal multiple access (NOMA), power allocation, multiple factors, imperfect successive interference cancellation (SIC).