tIn the atmospheric channel, the spatial correlation among the beams of wireless optical multiple input multiple output (MIMO) system caused by the antenna spacing and the channel fading can seriously affect the wireless optical communication system performance. We proposed a channel model for the correlative wireless optical MIMO channel based on the pulse position modulation (PPM), and the average channel capacity in lognormal fading channel is derived by using the Wilkinson method. The simulation results indicate that the average channel capacity is decreased due to the spatial correlation, and the effect is enhanced with the growth of the total energy. In addition, in a completely correlative channel, the impact of transmitter correlation on the channel capacity is more obvious than that of the receiver correlation.