Recently, the research on database outsourcing has been actively done with the popularity of cloud computing. However, because users' data may contain sensitive personal information, such as health, financial and location information, the data encryption methods have attracted much interest. Existing data encryption schemes process a query without decrypting the encrypted databases in order to support user privacy protection. On the other hand, to efficiently handle the large amount of data in cloud computing, it is necessary to study the distributed index structure. However, existing index structure and query processing algorithms have a limitation that they only consider single-column query processing. In this paper, we propose a grid-based multi column indexing scheme and an encrypted query processing algorithm. In order to support multi-column query processing, the multi-dimensional index keys are generated by using a space decomposition method, i.e. grid index. To support encrypted query processing over encrypted data, we adopt the Hilbert curve when generating a index key. Finally, we prove that the proposed scheme is more efficient than existing scheme for processing the exact and range query.