Electrical cables consist of numerous wires, the three-dimensional (3D) shape of which significantly impacts the cables’ overall properties, such as bending stiffness. Although X-ray computed tomography (CT) provides a non-destructive method to assess these properties, accurately determining the 3D shape of individual wires from CT images is challenging due to the large number of wires, low image resolution, and indistinguishable appearance of the wires. Previous research lacked quantitative evaluation for wire tracking, and its overall accuracy heavily relied on the accuracy of wire detection. In this study, we present a long short-term memory-based approach for wire tracking that improves robustness against detection errors. The proposed method predicts wire positions in subsequent frames based on previous frames. We evaluate the performance of the proposed method using both actual annotated cables and artificially noised annotations. Our method exhibits greater tracking accuracy and robustness to detection errors compared with the previous method.