A key capability of a long-term tracker is to search for targets in very large areas (typically the entire image) to handle possible target absences or tracking failures. However, currently there is a lack of such a strong baseline for global instance search. In this work, we aim to bridge this gap. Specifically, we propose GlobalTrack, a pure global instance search based tracker that makes no assumption on the temporal consistency of the target's positions and scales. GlobalTrack is developed based on two-stage object detectors, and it is able to perform full-image and multi-scale search of arbitrary instances with only a single query as the guide. We further propose a cross-query loss to improve the robustness of our approach against distractors. With no online learning, no punishment on position or scale changes, no scale smoothing and no trajectory refinement, our pure global instance search based tracker achieves comparable, sometimes much better performance on four large-scale tracking benchmarks (i.e., 52.1% AUC on LaSOT, 63.8% success rate on TLP, 60.3% MaxGM on OxUvA and 75.4% normalized precision on TrackingNet), compared to state-of-the-art approaches that typically require complex post-processing. More importantly, our tracker runs without cumulative errors, i.e., any type of temporary tracking failures will not affect its performance on future frames, making it ideal for long-term tracking. We hope this work will be a strong baseline for long-term tracking and will stimulate future works in this area.