The theoretical analysis of the bit error rate (BER) performance in a discrete Hartley transform (DHT) post-coded orthogonal frequency division multiplexing (OFDM) visible light communication (VLC) system over an additive white Gaussian noise (AWGN) channel is presented. The theoretical analysis results show that the proposed DHT post-coding scheme does not degrade the BER performance of the post-coded OFDM VLC systems. The analysis result is confirmed by our simulation results for random bit source. In addition, the peak-to-average power ratio (PAPR) of the DHT post-coded OFDM is evaluated by simulation. The simulation results show that DHT post-coding can greatly reduce of the PAPR of the optical OFDM system.