The continuous k-nearest neighbor query is one of the most important query types to share multimedia data or to continuously identify transportable users in LBS. Various methods have been proposed to efficiently process the continuous k-NN query. However, most of the existing methods suffer from high computation time and larger memory requirement because they unnecessarily access cells to find the nearest cells on a grid index. Furthermore, most methods do not consider the movement of a query. In this paper, we propose a new processing scheme to process the continuous k nearest neighbor query for efficiently support multimedia data sharing and transmission in LBS. The proposed method uses the patterns of the distance relationships among the cells in a grid index. The basic idea is to normalize the distance relationships as certain patterns. Using this approach, the proposed scheme significantly improves the overall performance of the query processing. It is shown through various experiments that our proposed method outperforms the existing methods in terms of query processing time and storage overhead.