In this paper, a lightweight design is carried out for the rectangular reflector of a small space telescope project. This study suggests a lightweight optimization design strategy based on three-point support in accordance with the high surface figure accuracy and low weight requirements of the project's rectangle reflective mirror. The fundamental structure of the mirror based on SiC material is first obtained, starting from the features of material selection and support method. Then, we get some parameters such as the radius-thickness ratio of the mirror through theoretical calculation and analysis, and preliminarily optimized these parameters. By using the maximization of the overall stiffness as the objective function, and the mirror RMS value as the design restraint, the topology optimization of the mirror is carried out. Finally, considering factors such as processing and manufacturing, we take the methods of size optimization to get an optimal structural model. Through simulation analysis, it can be measured that the weight of the mirror is only 3.94kg, the lightweight rate is 58%, and the RMS value in the X, Y, Z three axes under 1 g gravity condition is far less than 1/25λ(632.8nm) of the design index. This optimization method can well meet the design requirements. © 2023 SPIE.