In the design of mirror and its supporting structure in cryogenic environment, the surface accuracy under the temperature variation is an important factor affecting the performance of the space mirror. The surface shape RMS under the temperature change was taken as the performance index, and the surface shape variation of the space mirror was compared and studied based on the different supporting structures of the mirror manufactured by silicon carbide and the collocation forms of different materials. Firstly, the following two conditions of back support and lateral support were simulated and analyzed in cryogenic environment: (a) the mirror and the supporting structure was made of silicon carbide; (b) the mirror was made of silicon carbide and the supporting structure was made of other materials. Simulation analysis shows that the back support structure can obtain a better surface shape under condition (a), and the lateral support structure can obtain a better surface shape under condition (b). Then, the influence of the side supporting structure on the surface accuracy under different material matching conditions was studied. The relationship among the RMS and the CTE(coefficient of linear thermal expansion) of mirror material, the CTE of supporting structure materials, the absolute value of the difference between the CTE of mirror material land the CTE of supporting structure materials was analyzed using multivariate linear regression method. The analysis result shows that the absolute value of the difference between the CTE of mirror material and the CTE of supporting structure materials has greater influence on the RMS. The research results and ideas provide reference for the design of cryogenic optical mirror and its supporting structure in the future.