With the development of wireless communications and mobile computing technologies, the applications of moving objects have been developed in many topics, for example, traffic monitoring, mobile E-Commerce, Navigation System, and Geographic Information System. The feature of the moving objects is that objects change their locations continuously. Conventional spatial databases can not support to store the moving objects efficiently, because the databases must be updated frequently. Therefore, it is important to index moving objects for efficiently answering queries about moving objects. Among the spatial indexing methods for predicting current and future data, the approach of parametric spatial access methods has been applied largely, since it needs little memory space to preserve parametric rectangles, and it still provides good performance, so it is adopted generally. The methods of this approach include the TPR-tree, the TPR*-tree, the Bx-tree, and the Bxr-tree. Among those methods, the Bxr-tree improves CPU performance of TPR-tree by expanding query region first, and improves I/O performance of the Bxr-tree by expanding the data blocks additionally. However, the query process of the B$^x_r$-tree is too rough such that it costs too much CPU and I/O time to check the useless data. Therefore, in this thesis, we propose a new data structure and a new query processing method named Adjustable Expanded Index (AEI), to improve the disadvantages of the Bxr-tree. In our method, we let each block records the maximum and minimum speeds of each of eight directions, instead of only the maximum speed of each of four directions in the Bxr-tree method. Based on the data structure, the query region can be expanded in each of eight directions individually, instead of being expanded in each of four directions once in the Bxr-tree method. Moreover, in our AEI method, the data blocks can be expanded according to the direction toward the query region, instead of being expanded in four directions in the Bxr-tree method. In this way, the query process of AEI checks less number of data blocks because it considers the minimum speed of each of eight directions. Furthermore, the objects are divided into four groups in AEI according to their directions, while the Bxr-tree method does not. Only the objects moving to query region will be checked in the query process of AEI. Therefore, we can reduce more number of retrieved data blocks and the number of I/O operations in our method than the Bxr-tree. From our simulation, we show that the query process of the AEI method is more efficient than that of the Bxr-tree in term of the average numbers of retrieved data blocks and I/O operations.