For the large-aperture space telescope, the lightweight primary mirror design with a high-quality optical surface is a critical and challenging issue. This work presents a topology optimization-based design procedure for a lightweight primary mirror and a new mirror configuration of a large-aperture space telescope is obtained through the presented design procedure. Inspired by the topology optimization method considering cast constraints, an optimization model for the configuration design of the mirror back is proposed, through which the distribution and the heights of the stiffeners on the mirror back can be optimized simultaneously. For the purpose of minimizing the optical surface deviation due to self-weight and polishing pressure loadings, the objective function is selected as to maximize the mirror structural stiffness, which can be achieved by minimizing the structural compliance. The total mass of the primary mirror is assigned as the constraint. In the application example, results of the optimized design topology for two kinds of mass constraints are presented. Executing the design procedure for specific requirements and postprocessing the topology obtained of the structure, a new mirror configuration with tree-like stiffeners and a multiple-arch back in double directions is proposed. A verification model is constructed to evaluate the design results and the finite element method is used to calculate the displacement of the mirror surface. Then the RMS deviation can be obtained after fitting the deformed surface by Zernike polynomials. The proposed mirror is compared with two classical mirrors in the optical performance, and the comparison results demonstrate the superiority of the new mirror configuration.