This paepr presents an algorithm for searching an object in a fast way which contains a continuous moving object in multi-dimensional spatical databases. This algorithm improves the search method of R-tree for the case that a target object is continuously moving in a spatial database. It starts the searching from the current node instead of the root of R-tree. Thus, the algorithm will find the target object from the entries of current node or sibling nodes in the most cases. The performance analysis shows that it is more efficient than the existing algorithm for R-tree when search windows or target objects are continuously moving.