Multiple Input Multiple Output (MIMO) systems can improve the channel capability of an Optical Wireless Communication(OWC) system without adding extra frequency resources and emitting powers, but the space correlation between the channels will impact the system performance. This paper researches the effects of space correlation on the Bit Error Rate (BER) of an optical MIMO system in log-normal fading channel. In view of the Pulse Position Modulation (PPM), the log-amplitude fading matrix in different correlation mechanisms and maximum likelihood detection rule were derived by using an exponential correlation model in the log-normal fading channel. On the basis of this, the upper bound of the BER of correlated OWC MIMO system was deduced by adopting Wilkinson method. Finally, the impact of space correlation on BER of the OWC MIMO system was analyzed further. The results show that space correlation deteriorates the performance of OWC MIMO system and the BER of the system will be worsen by the space correction with the increase of the number of the antenna. It suggests that antennas should be placed reasonably to reduce the space correction between the antennas, so to better play the advantages of MIMO systems.