Graphs have been widely used for complex data representation in many real applications, such as social network, bioinformatics, and computer vision. Therefore, graph similarity join has become imperative for integrating noisy and inconsistent data from multiple data sources. The edit distance is commonly used to measure the similarity between graphs. The graph similarity join problem studied in this paper is based on graph edit distance constraints. To accelerate the similarity join based on graph edit distance, in the paper, we make use of a preprocessing strategy to remove the mismatching graph pairs with significant differences. Then a novel method of building indexes for each graph is proposed by grouping the nodes which can be reached in k hops for each key node with structure conservation, which is the k-hop tree based indexing method. As for each candidate pair, we propose a similarity computation algorithm with boundary filtering, which can be applied with good efficiency and effectiveness. Experiments on real and synthetic graph databases also confirm that our method can achieve good join quality in graph similarity join. Besides, the join process can be finished in polynomial time.