The fast steering mirror is a commonly used image motion compensation device in space cameras. The mechanical properties of the support structure will directly affect the response speed and closed loop bandwidth of the fast steering mirror system. A fast steering mirror driven by voice coil motor in a low earth orbit space camera was taken as the research object, and a two-axis flexible support structure based on cross-shaped flexible hinges was designed, which had the advantages of compact structure and small center drift. According to the approximate differential equation of cantilever beam deflection, the mathematical model of the rotational stiffness of the two-axis flexible support was established. The main structural parameters of the flexible hinge were selected for the resonant frequency requirements of the fast steering mirror mechanism, and a modal analysis of the mechanism was performed by using the finite element software MSC.Patran. The analysis results show that the resonant frequency of the fast steering mirror mechanism in the two working directions is 18.6 Hz and 18.7 Hz, while the resonant frequencies in other non-working directions are above 292.2 Hz, which proves that the choice of flexible hinge structural parameters is reasonable. In order to test the correctness of the theoretical model, a prototype of the fast steering mirror was processed and the experimental platform was built. The rotational stiffness and resonant frequency of the mechanism were tested. The results of the test and the theoretical analysis are consistent within the allowable error range.