Compressive sensing (CS) is an attractive technique to mitigate the high peak-to-average power ratio (PAPR) in optical orthogonal frequency division multiplexing (OFDM) systems. The lower computational complexity, easy implementation, and lack of side information requirement make signal compression an appropriate approach for PAPR reduction in both original and optical OFDM systems. We propose the CS approach for compressing the time-domain DC-biased optical OFDM (DCO-OFDM) signals at the transmitter side and multiple measurement vectors (MMV) based on orthogonal matching pursuit (OMP) algorithm to reconstruct the original signals at the receiver end. Simulations are conducted for QPSK and 16-QAM modulated symbols, and the results indicate that the PAPR of compressed signals is significantly reduced compared with the PAPR of the original DCO-OFDM signals. Furthermore, using the MMV-OMP algorithm and only about 1 dB additional signal-to-noise ratio, the original symbols are reconstructed at the receiver end without deteriorating the bit error rate performance.