Visible light communication (VLC) with non-orthogonal multiple access (NOMA) is one of the most promising technologies in wireless optical communication. To improve the system’s performance, we first proposed a NOMA-VLC system based on polar codes. Second, to evaluate the effect of power allocation algorithm on the transmission quality of the NOMA-VLC system based on polar codes, the performance of the NOMA-VLC system under a fixed power allocation algorithm was studied. Finally, considering the time-varying characteristics of wireless channels and users’ service quality, a quality of service (QoS)-based dynamic power allocation algorithm was proposed. In the dynamic power allocation algorithm, we prioritized the QoS of user1 (the user with a lower channel gain) by ensuring that the transmission rate of user1 was always greater than or equal to the minimum transmission rate, and the remaining power was allocated to users with higher channel gains to maximize the total transmission rate. Compared with the NOMA-VLC system without polar codes, simulation results show that user1 obtained 4.1 dB gain for the polar-coded NOMA-VLC system, when the bit error rate was 10 ^{− 4} and α = 1 / 9. And the total transmission rate of the proposed dynamic power allocation algorithm improved by 38.2% compared with the fixed power allocation algorithm with α = 1 / 9 and improved by 48.1% compared with the gain ration power allocation (GRPA) algorithm, when the signal-to-noise ratio was 10 dB. In addition, compared with the fixed power allocation algorithm with α = 1 / 9 and the GRPA algorithm, the outage probability performance of user2 (the user with a higher channel gain) was significantly improved, whereas the outage probability of user1 was basically unchanged under the dynamic power allocation algorithm.