Time-lapse microscopy provides an unprecedented opportunity to monitor single-cell dynamics. However, tracking cells for long periods remains a technical challenge, especially for multi-day, large-scale movies with rapid cell migration, high cell density, and drug treatments that alter cell morphology/behavior. Here, we present EllipTrack, a global-local cell-tracking pipeline optimized for tracking such movies. EllipTrack first implements a global track-linking algorithm to construct tracks that maximize the probability of cell lineages. Tracking mistakes are then corrected with a local track-correction module in which tracks generated by the global algorithm are systematically examined and amended if a more probable alternative can be found. Through benchmarking, we show that EllipTrack outperforms state-of-the-art cell trackers and generates nearly error-free cell lineages for multiple large-scale movies. In addition, EllipTrack can adapt to time- and cell-density-dependent changes in cell migration speeds and requires minimal training datasets. EllipTrack is available at https://github.com/tianchengzhe/EllipTrack.