This article aiming at the high performance requirements of the space camera mirror assembly, and in order to ensure that the space camera main mirror has good surface shape accuracy and high first-order natural frequency, the mirror and flexible support structure are studied and designed. First, according to the selection principle of the mirror material, SiC is selected as the mirror blank material of the mirror. According to the empirical formula, the three-point support scheme on the back of the mirror and the structural size parameters of the mirror body are determined. And a flexible support structure with multi-axis flexible hinge and dual-axis flexible hinge in series is designed for the mirror. Finally, the parameter optimization method is used to optimize the position radius of the mirror back support hole and the key dimensions of the flexible structure. The static analysis and modal analysis of the mirror assembly were carried out using the finite element method. The results show that the surface shape accuracy of the mirror is 0.015 lambda nm, the first-order natural frequency of the mirror is 145.57Hz, the weight is 135.35Kg, and the lightweight rate is 87.57%.