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We propose a novel index structure, the A-tree (Approximation tree), for the similarity search of high-dimensional data. The basic idea of the A-tree is the introduction of Virtual Bounding Rectangles (VBRs) which contain and approximate MBRs or data objects. VBRs can be represented rather compactly, and thus affect the tree configuration both quantitatively and qualitatively. First, since tree nodes can contain a large number of VBR entries, fanout becomes large, which leads to fast search. More importantly, we have a free hand in arranging MBRs and VBRs in tree nodes. In the A-trees, a node contains an MBR and its children VBRs. Therefore, by fetching a node of an A-tree, we can obtain the information of the exact position of a parent MBR and the approximate position of its children. We have performed experiments using both synthetic and real data sets. For the real data sets, the A-tree outperforms the SR-tree and the VA-File in all dimensionalities up to 64 dimensions, which is the highest dimension in our experiments. The A-tree achieves 77.3%(77.7%) fewer page accesses than the SR-tree (the VA-File) for 64-dimensional real data.