In this paper, we proposed a novel peak to average power ratio (PAPR) reduction scheme for the asymmetrically clipped optical orthogonal frequency division multiplexing (ACO-OFDM) visible light communications system. We implement the Toeplitz matrix based Gaussian blur method to reduce the high PAPR of ACO-OFDM at the transmitter and use the orthogonal matching pursuit algorithm to recover the original ACO-OFDM frame at the receiver. Simulation results show that for the 256-subcarrier ACO-OFDM system a ~6 dB improvement in PAPR is achieved compared with the original ACO-OFDM in term of the complementary cumulative distribution function, while maintaining a competitive bit-error rate performance compared with the ideal ACO-OFDM lower bound. We also demonstrated the optimal parameter C of 2 for the recovery algorithm based on the tradeoff between the data rate and recovery accuracy. The recovery results show that using the proposed scheme the ACO-OFDM can faithfully be reconstructed judging by the very low value for the reconstruct error of 0.06.