R-tree is an important multi-dimensional data structure widely employed in many applications for storing and querying spatial data. As GPUs emerge as powerful computing hardware platforms, a GPU-based parallel R-tree becomes the key to efficiently port R-tree-related applications to GPUs. However, traditional tree-based data structures can hardly be directly ported to GPUs, and it is also a great challenge to develop highly efficient parallel tree-based data structures on GPUs. The difficulty mostly lies in the design of tree-based data structures and related operations in the context of many-core architecture that can facilitate parallel processing. We summarize our contributions as follows: (i) design a GPU-friendly data structure to store spatial data; (ii) present two parallel R-tree construction algorithms and one parallel R-tree query algorithm that can take the hardware characteristics of GPUs into consideration; and (iii) port the vector map overlay system from CPU to GPU to demonstrate the feasibility of parallel R-tree. Experimental results show that our parallel R-tree on GPU is efficient and practical. Compared with the traditional CPU-based sequential vector map overlay system, our vector map overlay system based on parallel R-tree can achieve nearly 10-fold speedup.