There has been considerable interest in similarity join in the research community recently. Similarity join is a fundamental operation in many application areas, such as data integration and cleaning, bioinformatics, and pattern recognition. We focus on efficient algorithms for similarity join with edit distance constraints. Existing approaches are mainly based on converting the edit distance constraint to a weaker constraint on the number of matching q-grams between pair of strings. In this paper, we propose the novel perspective of investigating mismatching q-grams. Technically, we derive two new edit distance lower bounds by analyzing the locations and contents of mismatching q-grams. A new algorithm, EdJoin, is proposed that exploits the new mismatch-based filtering methods; it achieves substantial reduction of the candidate sizes and hence saves computation time. We demonstrate experimentally that the new algorithm outperforms alternative methods on large-scale real datasets unde...