The shape of query windows for spatial selection queries is a rectangle in many cases. However, it can be issued for spatial selection queries with not only rectangular query widow, but also polygonal query window. Moreover, as the applications like GIS can manage much more spatial data, they can support the more various applications. Therefore it is valuable for considering about the query processing method suitable for not only rectangle query window, but also general polygonal one. It is the general state-of-the-art approach to use the plane- sweep technique as the computation algorithm in the refinement step as the spatial join queries do. However, from the observation on the characteristics of spatial data and query windows, we can find in many cases that the shape of query window is much simpler than that of spatial data. From these observations, we suggest a new refinement process approach which is suitable for this situation. Our experiments show that, if the number of vertices composing the query window is less than about 20, the new approach we suggest is superior to the state-of-the-art approach by about 20% in general cases.