Non-orthogonal multiple access (NOMA) has recently attracted significant attention as a promising multiple access scheme for the 5th generation (5G) wireless communication due to its superior spectral efficiency, which has also been studied and shown to achieve a superior performance in visible light communication (VLC) networks. However, the error propagation (EP) problem due to successive interference cancellation (SIC) decoding has not yet been resolved, which degrades the system BER performance and causes user unfairness. In this work, symmetric superposition coding (SSC) and symmetric SIC (SSIC) decoding are proposed for a downlink NOMA-based VLC network, in which the distribution of the demodulation regions of the user allocated with more power will be symmetrical in terms of the decision threshold of the user allocated with less power. Furthermore, the proposed method is experimentally tested and the results show that more than 90% demodulation errors caused by EP are eliminated compared with traditional NOMA VLC.