This paper presents a method for implementing the ESM visual tracker proposed by Malis et al. on a GPU to realize fast and accurate visual tracking. The ESM tracker is effective especially for the images in which feature points are difficult to obtain, since it uses entire image pixels of the target image region. Although its ordinary CPU implementation runs fairly fast, our GPU implementation enables yet faster tracking, so that it runs even at 1000fps when used with a camera that can capture images at that frame rate. We analyze which parts of the algorithm can be processed in a parallel fashion, and implement them by appropriately using the memory system of a GPU. We show comparison between our GPU implementation and a CPU implementation of the ESM algorithm in terms of computation time and tracking performance.