R-trees are popular spatial indexing techniques that have been widely used in many geospatial applications. The increasingly available Graphics Processing Units (GPUs) for general computing have attracted considerable research interests in applying the massive data parallel technologies to index and query geospatial data based on R-trees. In this paper, we investigate on the potential of accelerating both R-tree bulk loading construction and R-tree based spatial window query on GPUs.  Experiments show that our proposed GPU-based parallel query processing implementation achieves 6x~18x speedup over serial CPU implementations and is 2X faster on average over 8-core CPU implementation using OpenMP. Our experiments also show that the speedups are significantly affected by R-tree qualities which warrants further investigations. Additional comparisons between the GPU R-tree implementation and a GPU single-level grid-file based indexing approach are performed to understand the relative advantages and disadvantages of the two popular spatial indexing approaches on GPUs.