The support structure between payloads is an important part of a space gravitational wave detection satellite, and its thermal stability will directly affect the interferometer’s measurement accuracy. However, due to temperature changes, the connecting structure between the loads will generate deformation, and a support structure with the coefficient of thermal expansion (CTE) of −1 × 10⁻⁶/K will thus need to be designed to counteract this thermal deformation. In order to solve this problem, this paper adopts the method of mutual offsetting of the thermal deformation of different materials to design a thermally stable support structure satisfying this negative CTE. The structure was optimized by the arithmetic of non-linear programming by the quadratic Lagrangian hybrid algorithm (NLPQL), and the structural parameter satisfying the CTE of −1.008 × 10⁻⁶/K was obtained. Meanwhile, the effect of the change in the thermal expansion coefficient of each material on the overall structure under this parameter was sampled and calculated. Moreover, the experimental results show that the CTE of the support structure under the optimized parameters was −1.114 × 10⁻⁶/K, which differs from the simulation results by 9.5%.