A biaxial bipod flexible support structure was designed based on flexibility analysis parameter optimization to improve the accuracy of a mirror surface subject to ambient temperature fluctuations. First, the flexibility of the mirror support structure was calculated and analyzed, and a flexibility formula for the leg-and-mirror assembly was deduced. Then, to ensure the axial support stiffness and unloading ability of the mirror, a set of flexible support structure size parameters were calculated with a diameter of 200 mm. Finally, the flexibility formula, dynamic characteristics, and temperature adaptability of the support structure were analyzed and verified by finite element analysis and vibration tests. The results show that the error between the theoretical and finite element analysis values is less than 10%, under a certain force. The first-order frequency of the component, obtained by the vibration test, is 358.5 Hz, and the relative error of the theoretical calculation is 89%. At a temperature difference of 20 ℃, the value of the mirror surface accuracy is 0.8. The validity of the theoretical model was verified, thus proving that the bipod flexible support structure can reduce the influence of temperature fluctuation on a mirror surface.