The similarity join is an important building block for similarity search and data mining algorithms. In this paper, we propose an algorithm for similarity join on Graphics Processing Units (GPUs). As major advantages GPUs provide extremely high parallelism combined with a high bandwidth in data transfer to main memory. To exploit these advantages for similarity join, we propose an index structure designed for the specific environment of GPU. Experiments demonstrate massive performance gains of our method over conventional similarity join on CPU and significant further speed-up by index support.