According to the requirements of ultra-light and high thermal stability of a space camera, an integrated backplate structure is designed so that the supporting backplate is not only the backplate of the main mirror, but also the main bearing plate of the space camera. The SiC with high specific stiffness and high thermal stability is used as the backplate material. The layout of back ribs is determined by the variable density topology optimization with the addition of a minimum size constraint. The size optimization design is completed by a multi-objective optimization model with Non-dominated Sorting Genetic Algorithm II (NSGA-II), integrating the mirror surface shape and the mass of the backplate. The mass of the backplate is only 0.591 kg and the minimum rib thickness is 2.1 mm. The dynamic and static performances of the optimization results are finally analyzed by the finite element analysis. The results show that the root-mean-square value of the mirror shape in the mirror assembly is 0.158 nm under a temperature rising load of 5 °C, which means good thermal stability. The root-mean-square value of the mirror shape is 1.169 nm and the peak to valley value is 5.403 nm under the X-direction gravity load (the direction perpendicular to the optical axis/the direction of detecting surface shape). The first-order intrinsic frequency of the mirror assembly is 397 Hz and the random vibration response value of the sampling point of the mirror edge is less than 16g. These mean the requirements for space application are satisfied.