Visible light communication (VLC) using optical sources which can be simultaneously utilized for illumination and communication is currently an attractive option for wireless personal area network. Improving the data rate in optical wireless communication system is challenging due to the limited bandwidth of the optical sources. In this paper, we design the singular value decomposition (SVD)- based multiplexing multiple-input multiple-output (MIMO) system to support two data streams in optical wireless channels. Noting that the conventional allocation method in radio frequency (RF) MIMO channels cannot be applied directly to the optical intensity channels, we propose a novel method to allocate the optical power, the offset value and the modulation size for maximum sum rate under the constraints of the nonnegativity of the modulated signals, the aggregate optical power and the bit error rate (BER) requirement. The simulation results show that the proposed allocation method gives the better performance than the method to allocate the optical power equally for each data stream.