In order to obtain a mirror with low mass, high stiffness and high surface accuracy, a topology optimization method with minimum compliance as optimization objective and mirror weight as constraint condition is proposed. Firstly, an optimization model including stiffness optimization model, mass minimization model and sensitivity analysis is constructed. Secondly, on the basis of this theoretical model, the optimization design of 450mm×290mm×60mm long strip SiC mirror is carried out. Finally,the simulation analysis of the structure optimized model is carried out, and the model is compared with the traditional design scheme. The results show that its performance is better than the traditional design scheme. This study provides an effective design method for the subsequent design of the same type mirrors.