According to the performance requirements of a high-resolution space camera for the bottom support structure, a flexible and damping support structure composited by a fillet feet frame and a straight beam was designed. Firstly, the bottom supporting structure of the space camera was designed based on the request of a satellite structure, and a optimized design model for the random response was established. The flexible link for the leg of two-feet frame structure was proposed with the size optimization technology, and the minimum thickness of the flexible link is 2.5 mm. Then, the support structure at the bottom of the camera was analyzed in engineering. The analysis results show that the weight of support structure components is 1.26 kg, and the fundamental frequency is 1 624 Hz. Finally, the support structure components of the space camera were tested by the random vibration test, obtained results show that the structure joint maximum response RMS value of the camera is 21.4 grms, and the random response maximum relative magnification is 0.93, satisfying the requirement of the support structure vibration of the space camera. These results verify the reliability of the design and analysis in this paper and provide a guiding for design of camera support structures of similar satellites.