Efficient indexing techniques have been developed for the exact and approximate substructure search in large scale graph databases. Unfortunately, the retrieval problem of structures with categorical or geometric distance constraints is not solved yet. In this paper, we develop a method called PIS (Partition-based Graph Index and Search) to support similarity search on substructures with superimposed distance constraints. PIS selects discriminative fragments in a query graph and uses an index to prune the graphs that violate the distance constraints. We identify a criterion to distinguish the selectivity of fragments in multiple graphs and develop a partition method to obtain a set of highly selective fragments, which is able to improve the pruning performance. Experimental results show that PIS is effective in processing real graph queries.