We present a pedestrian tracking algorithm, DensePeds, that tracks individuals in highly dense crowds (greater than 2 pedestrians per square meter). Our approach is designed for videos captured from front-facing or elevated cameras. We present a new motion model called Front-RVO (FRVO) for predicting pedestrian movements in dense situations using collision avoidance constraints and combine it with state-of-the-art Mask R-CNN to compute sparse feature vectors that reduce the loss of pedestrian tracks (false negatives). We evaluate DensePeds on the standard MOT benchmarks as well as a new dense crowd dataset. In practice, our approach is 4.5 times faster than prior tracking algorithms on the MOT benchmark and we are state-of-the-art in dense crowd videos by over 2.6% on the absolute scale on average.