The imaging quality of space infrared telescope depends on the cryogenic environment. In this environment, strict requirements are placed on the structure of the mirror and its supporting structure. The current passive supporting structures of telescopes at home and abroad (such as bipod, hexapod and whiffle-tree structures) are introduced, and then the active supporting structure forms of domestic and foreign telescopes and the principle of actuators are analyzed and explained. Through the analysis of the active and passive supporting structures of domestic and foreign telescopes, the two are compared, and their advantages, disadvantages and applicable fields are pointed out. Two methods for realizing athermalized supporting structure are proposed. For the segmented telescope, the combined supporting form of whiffle-tree structure and actuator is used. For the monolithic telescope, the combined supporting form of whiffle-tree structure, A-frame structure and actuator is used.