Traditional orthogonal frequency division multiplexing (OFDM) based visible light communication (VLC) system is susceptible to high peak-to-average power ratio (PAPR), thus leading to low power efficiency. To address this issue, a sparse code multiple access (SCMA) codebook design method has been proposed to lower the PAPR of the clipping based OFDM-VLC system. Then, the codebooks of the high-dimension mother constellation (MC) and low-dimension MC are optimized, respectively. Specifically, for high-dimension MCs like T16-quadrature amplitude modulation (T16-QAM), the constellation points (CLPs) with higher transmit power are mapped to the CLPs with lower power. For low-dimension MCs like 4-pulse amplitude modulation (4-PAM), a contracted mapping method is proposed to reduce the power of the CLPs located on the real axis of the MC. Simulations show that the proposed method could achieve better PAPR performance for any value of the clipping ratio with only a slight bit error rate (BER) performance loss compared to the original codebook design. Besides, the smaller clipping ratio would induce better PAPR performance but worse BER performance.Moreover, the increasing number of iterations in the logarithm domain message passing algorithm (log-MPA) could improve the BER performance. This work will benefit the research and development of SCMA-OFDM-VLC systems.