Abstract: In order to meet the needs for the performance of the primary-fourth double-sided integrated mirror in a certain on-axis four-mirror infrared optical system, the mirror body needs to have higher stiffness with high lightweight rate to keep the two mirror face shapes stable. The topology optimization method was used to optimize the initial model of double-sided integrated mirror with the maximum stiffness was set as the optimization objective, and the volume fraction of the design domain was constrained. The optimization results show that the stiffness is higher while the primary mirror and the fourth mirror are connected through ribbed plate arranged radially around the optical axis. The optimal size parameters for the primary-fourth and ribbed plate were obtained by free size optimization. Based on the optimization results, the primary-fourth double-sided integrated mirror was designed, and the lightweight rate achieved 82.4% by using the final solution. The mode of the primary-fourth double-sided integrated mirror and the influence of 1 g gravity on the root-mean-square (RMS) of the surface shape were analyzed, a first-order mode frequency achieved 417 Hz, and the maximum change of surface shape under gravity was 1/22 λ （λ= 632.8 nm). The analysis results show that the optimized mirror body has sufficient stiffness and good resistance to the deformation under gravity. The mirror was processed and tested according to the final design, and the measured results show that the RMS of primary-fourth mirror surface shapes are both about λ/7, which meets the needs for the performance of infrared optical systems, proves the effectiveness of this topology optimization design method, and provides some references for the optimization design of double-sided integrated mirrors.