Non-orthogonal multiple access (NOMA) can increase the overall spectral efficiency of visible light communication (VLC) system. In this paper, we proposed a novel scheme to improve the bit error rate (BER) performance of a two-user NOMA VLC system by adjusting superposition constellation. The corresponding closed-form BER expressions are derived. Convex optimization is used to find the optimal parameters of the adjusted superposition constellation, where the overall BER is minimized. The BER performances are evaluated by theoretical analysis, Monte-Carlo (MC) simulation and experiment. The results illustrate that 8.9-dB and 8.1-dB signal-to-noise ratios (SNRs) are reduced to achieve BER of 10-3 for the two users, whose power allocation coefficients are 0.6 and 0.4, respectively.