Due to only the intensity of a signal is used to carry information, optical wireless systems are constrained to send real and positive values at the optical transmitter. Therefore, the conventional OFDM cannot be directly applied in optical systems. To combat multipath distortion, several modified OFDM systems have been studied, such as DC-biased optical OFDM (DCO-OFDM), asymmetrically clipped optical OFDM (ACO-OFDM), Flip-OFDM and Unipolar OFDM (U-OFDM), etc. In order to transmit real signal in optical environments, there is a Hermitian symmetric constraint with discrete Fourier transform (DFT), or discrete Hartley transform (DHT) without the Hermitian requirement. In this paper, we propose a novel OFDM system, namely Position Modulating OFDM (PM-OFDM), which utilizes DFT but removes the Hermitian constraint. Two receiver structures will be presented with different complexities and performance. The proposed PM-OFDM outperforms the existing systems in terms of bit-error-rate (BER) and complexity, with the same spectral efficiency.