With the rapid development of space exploration, space debris has attracted more attention due to its potential extreme threat, leading to the need for real-time and accurate debris tracking. However, existing methods are mainly based on traditional signal processing, which cannot effectively process the complex background and dense space debris. In this paper, we propose a deep learning-based Space Debris Tracking Network~(SDT-Net) to achieve highly accurate debris tracking. SDT-Net effectively represents the feature of debris, enhancing the efficiency and stability of end-to-end model learning. To train and evaluate this model effectively, we also produce a large-scale dataset Space Debris Tracking Dataset (SDTD) by a novel observation-based data simulation scheme. SDTD contains 18,040 video sequences with a total of 62,562 frames and covers 250,000 synthetic space debris. Extensive experiments validate the effectiveness of our model and the challenging of our dataset. Furthermore, we test our model on real data from the Antarctic Station, achieving a MOTA score of 73.2%, which demonstrates its strong transferability to real-world scenarios. Our dataset and code will be released soon.