The performance analysis of a novel optical modulation scheme is presented in this paper. The basic concept is to transmit signs of modulated optical orthogonal frequency division multiplexing (O-OFDM) symbols and absolute values of the symbols separately by two information carrying units: 1) indices of two light emitting diodes (LED) transmitters that represent positive and negative signs separately; and 2) optical intensity symbols that carry the absolute values of signals. The new approach, referred as to non-DC-biased OFDM (NDC-OFDM), uses the optical spatial modulation (OSM) technique to eliminate the effect of the clipping distortion in DC-biased optical OFDM (DCO-OFDM). In addition, it can achieve similar advantages as the conventional unipolar modulation scheme, asymmetrically clipped optical OFDM (ACO-OFDM), without using additional subcarriers. In this paper, the analytical BER performance is compared with the Monte Carlo result in order to prove the reliability of the new method. Moreover, the practical BER performance of NDC-OFDM with DCO-OFDM and ACO-OFDM is compared for different constellation sizes to verify the improvement of NDC-OFDM on the spectral and power efficiencies.