A string similarity join finds similar pairs between two collections of strings. Many applications, e.g., data integration and cleaning, can significantly benefit from an efficient string-similarity-join algorithm. In this paper, we study string similarity joins with edit-distance constraints. Existing methods usually employ a filter-and-refine framework and suffer from the following limitations: (1) They are inefficient for the data sets with short strings (the average string length is not larger than 30); (2) They involve large indexes; (3) They are expensive to support dynamic update of data sets. To address these problems, we propose a novel method called trie-join, which can generate results efficiently with small indexes. We use a trie structure to index the strings and utilize the trie structure to efficiently find similar string pairs based on subtrie pruning. We devise efficient trie-join algorithms and pruning techniques to achieve high performance. Our method can be easily extended to support dynamic update of data sets efficiently. We conducted extensive experiments on four real data sets. Experimental results show that our algorithms outperform state-of-the-art methods by an order of magnitude on the data sets with short strings.