This paper proposes an optimal receive algorithm for asymmetrically clipped optical OFDM (ACO-OFDM) based optical wireless communication systems with intensity modulation and direct detection (IM/DD). Conventional ACO-OFDM system only employs the information of odd subcarriers, and the information on even subcarriers is discarded. This paper presents a novel ACO-OFDM receiver, which exploits the anti-periodic property of time domain signal. Analysis results show that power efficiency and bit error ratio (BER) performance are improved. Besides, a parameter is introduced to decide the clipping position, and the performance can be further improved. Simulation results show that the BER performance of proposed optimal receive algorithm can be improved more than 2 dB.