The figure shape precision of primary mirrors are most important for the imaging quality of space cameras. To ensure a space camera to have high imaging quality in a wide temperature range (20±10℃), a flexible support structure is designed. Firstly, the SiC material is selected to make the mirror and semi-enclosed type light-weight processing is carried out for the back of the primary mirror body. Secondly, for the environment in the temperature range of 20±10℃ in which the round primary mirror module with an aperture of 550 mm will be used, a flexible articulated structure is designed. Because the parameters of the supporting structure are optimized by the Matlab software, the flexible supporting structure has enough radial flexibility and can absorb distortion so as to reduce the stress of the mirror. The finite element analysis result shows that the supporting structure has the first-order frequency of 267 Hz which is much higher than the inherent frequency of the mirror body module. So, it can ensure the primary module not to be damaged. Even when the gravitation is coupled with the temperature load of 10℃, the mirror can meet the requirement of the figure shape error (RMS) less than λ/40 of the optical system.