Core-Periphery structure, as a critical mesoscale structure, is commonly found in diverse real-world networks, in which nodes are endogenously categorized as core or peripheral nodes by the underlying interconnection patterns. It plays an important role in sustaining the intrinsic order and functional behavior of networked systems. However, despite the study on inherent core–periphery vulnerabilities to node removals, little is known on the core–periphery robustness when networks are suffering from the attacks that happen on links between nodes, especially for the more practical situations where attackers have limited ability to obtain precise network information. In this paper, a novel index is proposed for measuring the capacity of the core–periphery structure to resist link-based attacks. By introducing an attack precision parameter, we establish a unified evaluation framework for link-based attacks with imprecise information, which divides attack behaviors into localized attacks and non-localized attacks, and treats the usual random attacks and targeted attacks as the two special situations of our non-localized case. Several enhancing algorithms guided by our index with local search strategy are exquisitely devised, and experimental results are provided to demonstrate the efficacy of our framework and algorithms that remarkably improve the core–periphery robustness against link-based attacks with imprecise information.