In view of the functional requirements of high surface shape error accuracy, high reliability and high stability of mirror support for space remote sensor, a three-point back support structure applied in the mirror support in the field of space was designed, the back support structure included taper sleeve, flexible segment and adjusting pad. The in-depth study was done about support principle and engineering realization of the three-point back support structure. The error source which caused the variation of surface shape error of the three-point back supporting mirror component was summarized, the theory of surface shape variation caused by various error sources was studied, and the corresponding design of the supporting structure was carried out to alleviate the variation of the surface shape error of the mirror caused by various error sources. Firstly, the static and dynamic simulation of the design results were carried out by means of finite element analysis, then the assembled and processed mirror assembly was tested. The results show that the surface shape error of mirror with the three-points support structure is better than λ/60(λ=632.8 nm), the rigid body displacement of mirror is smaller than 0.01 mm, the dip angle is smaller than 2″, the mass of the mirror component is smaller than 4.5 kg. The component has a reasonable distribution of modal, the fundamental frequency is 254 Hz, which is higher than the requirement of 120 Hz. The maximum magnification rate of the mirror assembly under sine vibration and random vibration is 1.73 times, and the maximum stress under sine vibration and random vibration is 369 MPa, far lower than the yield limit of the selected material.