We present a fast motion detection technique in a crowd as an abnormal motion based on optical flow and a motion history image (MHI). Since a camera view is usually not in perpendicular with motion direction, the velocity of motion is not uniform spatially. Instead of object detection directly from an image, we separate an image into several blocks. In this paper, we propose a novel method to analyze a motion using MHI representation, called a shift space and a shift histogram. Together with a velocity histogram, the method can detect fast motion in a crowd, realizing local abnormal event detection. The performance of the proposed method is experimentally illustrated and evaluated.