For the space-constrained underwater installations, spatial correlation is an essential factor affecting the reliability of the underwater optical wireless communication (UOWC) system with multiple-input multiple-output (MIMO) technology. In this paper, a joint optimization method for the layout and transmit power allocation of the light-emitting diode (LED)-based UOWC system is proposed and demonstrated under the weak turbulent channel. To analysis the transmission performance of the MIMO UOWC system, a composite channel model incorporating absorption, scattering and weak turbulence effects is established, and the channel spatial correlation characteristics with various system parameters is analyzed based on this model. Among these parameters, we take a 9×9 MIMO UOWC system as an example to simulate the communication performance of the optimization method under different turbulence intensities. The simulation results show the optimized system exhibits a channel capacity improvement of 13bps/Hz compared to the original system at the signal-to-noise ratio (SNR) of 20dB and the same turbulence intensity. Moreover, the SNR of jointly optimized system can achieve a gain of 5dB at the same bit error rate (BER). By extending the joint optimization algorithm to a 16×16 MIMO UOWC system, the optimized SNR can also obtain a gain of 7.5 dB which effectively demonstrates the universality of the proposed joint optimization algorithm.