a conceptual lightweight rectangular mirror is designed based on the theory of topology optimization and the specific structure size is determined through sensitivity analysis and size optimization in this paper. under the load condition of gravity along the optical axis, compared with the mirrors designed by traditional method using finite element analysis method, the performance of the topology optimization reflectors supported by peripheral six points are superior in lightweight ratio, structure stiffness and the reflective surface accuracy. this suggests that the lightweight method in this paper is effective and has potential value for the design of rectangular reflector.