To meet the requirements of high location accuracy and surface figure accuracy for rectangular space mirror, and to reduce mirror weight extremely at the same time, became the new and important research subject in most countries. The material selection, support form, geometry parameters and lightweight structure form are taken into account in the design of a rectangular space mirror. Putting forward the topology optimization ensures the mirror back lightweight form. By using finite element analysis technique, the static stiffness of the mirror is analyzed. The analysis results show that: the surface accuracy reaches λ/10 PV，λ/50 RMS (λ=632.8 nm) under gravity load, PV value is 7nm, RMS values is 1.68 nm, and the mirror component first-order natural frequency is 256 Hz, which is better than traditional structure forms of mirrors, and can meet the application requirements.