We consider optical wireless communication which can be utilized for illumination and communication by relying on lighting devices. Due to the limited bandwidth of optical sources, it is challenging to achieve high data rate in optical wireless systems. In order to obtain a multiplexing gain and high spectral efficiency, we design an optical multi-input multi-output (MIMO) system utilizing a singular value decomposition-based spatial multiplexing and adaptive modulation. We note that the conventional allocation method in radio frequency MIMO channels cannot be applied directly to the optical intensity channels. In this paper, we generalize the result of power allocation method in  for arbitrary number of transmit and receive antennas in optical wireless MIMO systems. Based on three constraints, namely, the nonnegativity, the aggregate optical power, and the bit error rate requirement, we propose a novel method to allocate the optical power, the offset value, and the modulation size for maximum sum rate. From some selected simulation results, we show that our proposed allocation method gives a better spectral efficiency than the method that allocates the optical power equally for each data stream.