A flexible support structure was proposed to keep higher surface figure accuracy of space mirrors under gravity and uniform temperature change load cases. According to the optical design requirements, the structural form of a mirror was determined, and then a flexible support structure of the primary mirror was designed. By adopting finite element analysis software, the mirror component was analyzed and its structure was optimized. Analysis results show that the first order natural frequency of the mirror component is 179 Hz, and the surface figure accuracy RMS of the mirror reaches 5.06, 4.43 and 7.59 nm when gravity load is applied in the directions of X, Y, and Z axes respectively. Furthermore,the integrated surface figure accuracy RMS of the mirror reaches 6.08, 6.32 and 8.08 nm respectively under the load cases of gravity in three directions coupled with uniform temperature rise of 4 ℃. Laboratory test results indicate that the mirror can offer a good image quality under the condition of 4 ℃ uniform temperature change, the mechanical test results are consistent with that of the theoretical analysis and the change of the surface figure accuracy is not obvious after dynamic and thermal vacuum tests. Analysis and experimental results demonstrate that designs of the mirror and its support structure are effective, which can meet the requirements of space applications.