The reflective surface accuracy (RSA) of traditional space mesh antennas typically ranges from 0.2 to 6 mmRMS. To improve the RSA, an active control scheme can be employed, although it presents challenges in determining the installation position of the actuator. In this study, we propose a novel design for a semi-rigid cable mesh that combines rigid members and a flexible woven mesh, drawing inspiration from both rigid ribbed antennas and biomimicry. Initially, we investigate the planar mesh topology of spider webs and determine the bionic cable surface’s mesh topology based on the existing hexagonal meshing method, with RSA serving as the evaluation criterion. Subsequently, through motion simulations and careful observation, we establish the offset angle as the key design parameter for the bionic mesh and complete the design of the bionic cable mesh accordingly. Finally, by analyzing the impact of the node quantity on RSA, we determine a layout scheme for the flexible woven mesh with a variable number of nodes, ultimately settling for 26 nodes. Our results demonstrate that the inclusion of numerous rigid components on the bionic cable mesh surface offers viable installation positions for the actuator of the space mesh antenna. The reflector accuracy achieved is 0.196 mmRMS, slightly surpassing the lower limit of reflector accuracy observed in most traditional space-space mesh antennas. This design presents a fresh research perspective on combining active control schemes with reflective surfaces, offering the potential to enhance the RSA of traditional rigid rib antennas to a certain extent.