In autonomous driving, state-of-the-art methods detect pedestrian through appearance in 2-D spatial images. However, these approaches are typically time-consuming because of the complexity of algorithms to cope with large variations in shape, pose, action, and illumination. They also fall short of capturing temporal continuity in motion trace. In a completely different approach, this work recognizes pedestrians along with their motion directions in a temporal way. By projecting a driving video to a 2-D temporal image called Motion Profile (MP), we can robustly distinguish pedestrian in motion and standing-still against smooth background motion. To ensure non-redundant data processing of deep network on a compact motion profile further, a novel temporal-shift memory (TSM) model is developed to perform deep learning of sequential input in linear processing time. In experiments containing various pedestrian motion from sensors such as video and LiDAR, we demonstrate that, with the data size around 3/720th of video volume, this motion-based method can reach the detecting rate of pedestrians at 90% in near and mid-range on the road. With a super-fast processing speed and good accuracy, this method is promising for intelligent vehicles.