In order to overcome the impacts on Space Optical Communication System brought by the turbulent in the atmosphere, the multi-transmitting technology, i.e. the space diversity technology is adopted in Space Optical Communication System to improve its properties at a lower cost such as reducing the error rate and raising its reliabilities. However, with the increase of correlations among the diversity signals, the validities of space diversity technologies decrease. On this condition, the adaptive diversity technology can be introduced to elevate the signal-to-noise rate. Under the condition of receiving correlative signals, with the help of combining selection diversity with adaptive signal processing technology, in this paper the SD-LMS (Selection Diversity-Least Mean Square) adaptive signal-processing algorithm is advanced. The following result could be obtained through the theoretical analysis: the signal-to-noise of outputting signals will be raised with the increase of the numbers of the diversity inputting signals, and the outputting signal distortion is similar to that of the single-way inputting signals. The simulating experiments show that SD-LMS adaptive signal-processing algorithm can significantly improve the properties of the outputting signals. The most prominent characteristics of the SD-LMS adaptive signal-processing algorithm is that it can automatically adjust the optimal weight factors of the adaptive filtering, and adapt itself to any changes of the noise without specially evaluating the properties of channels and noise.