Optical orthogonal frequency division multiplexing (O-OFDM) has been widely adopted as a high-speed data transmission technique in visible light communication systems. This technique usually suffers from high peak-to-average-power ratio (PAPR). In this paper, a new PAPR reduction technique is proposed for O-OFDM signals. At the transmitter, a matrix transformation with the Gaussian elements is applied to the time-domain O-OFDM signal and at the receiver, the inverse matrix is used to recover the original signal. We show that the Gaussian orthogonal matrices can reconstruct the original signals without degrading the bit error rate (BER) performance. Gram-Schmidt technique is used to orthogonalize the Gaussian matrices. Computer simulations are conducted for 16-QAM baseband modulated symbols and about 3 dB PAPR reduction gain is achieved by the proposed approach compared with conventional O-OFDM.