To decrease the single installation point acceleration response RMS(Root Mean Square) of a micro-satellite for earth observation, this paper presents a topology optimization method for satellite primary load bearing structure to minimize the acceleration response RMS. Firstly, the design scheme of the entire satellite is analyzed by finite element simulation. The results suggest that the acceleration response RMSs of some component installation points are too large and failed to meet the design requirements. By sensitivity analysis, it points out that the backplane is a key element for the acceleration response RMS of Gaussian random vibration. By adopting the method of topology optimization for a continuous body, the satellite model is optimized and a new model that fully meets the design requirements is obtained by taking the acceleration response RMS as an objective function and the volume as a restrict condition. Finally, both the finite element simulation and Gaussian random vibration are performed. It indicates that the parameters of new satellite primary load bearing structure meet design requirements, and among them, the acceleration response RMSs of some key component installation points like star sensors, storage battery and source controllers have reduced at least 23.3%, 10.6%, 11.3%, respectively. These results verify the feasibility and effectiveness of the proposed optimized topology.