<p>With the development of quantum computers, Quantum Key Distribution (QKD) networks are attracting attention as a novel solution to guarantee information security in the post-quantum era. Routing protocols play a crucial role in improving the quality of communication services in QKD networks. The fluctuation of link states in QKD networks due to the fluctuation of communication demand and environmental factors is an important factor that cannot be ignored in QKD network routing design. Most of the existing QKD network routing protocols selected paths based on the current link state information. Since the fluctuation of the link state is not taken into account, it greatly affects the quality of service of the network in robustness. To address the above issues, this paper employs the distributionally robust optimization method in the design of routing protocols to enhance the robustness of routing paths to the link state fluctuations. In addition, since the original path solving equation of the proposed robust QKD routing protocol is NP-hard to solve, this paper further reformulates it into a tractable form by the scenario approximation method based on dual conversion. Finally, the results of simulation experiments show that the proposed robust QKD routing protocol achieves a significant performance improvement over existing deterministic routing protocols, with increases of 17% in bandwidth, 22% in worst-case bandwidth, and a 15% reduction in communication blocking rate. By considering the fluctuation of link states, the proposed routing protocol achieves a significant performance improvement, which is of great significance in advancing the development of QKD networks.</p>