Emerging modem database applications require multi-dimensional index structures to provide high performance for data retrieval. In order for a multi-dimensional index structure to be integrated into a commercial database system, efficient techniques that provide transactional access to data through this index structure are necessary. The techniques must support all degrees of isolation offered by the database system. Especially degree 3 isolation, called "no phantom read," protects search ranges from concurrent insertions and the rollbacks of deletions. In this paper, we propose a new phantom protection method for multi-dimensional index structures that uses a multi-level grid technique. The proposed mechanism is independent of the type of the multi-dimensional index structure, i.e., it can be applied to all types of index structures such as tree-based, file-based, and hash-based index structures. In addition, it has a low development cost and achieves high concurrency with a low lock overhead. It is shown through various experiments that the proposed method outperforms existing phantom protection methods for multi-dimensional index structures.