As GML is becoming the de facto standard for geographic data storage, transmission and exchange, more and more geographic data exists in GML format. In applications, GML documents are usually very large in size because they contain a large number of verbose markup tags and a large amount of spatial coordinate data. In order to speedup data transmission and reduce network cost, it is essential to develop effective and efficient GML compression tools. Although GML is a special case of XML, current XML compressors are not effective if directly applied to GML, because these compressors have been designed for general XML data. In this paper, we propose GPress, a compressor for effectively compressing GML documents. To the best of our knowledge, GPress is the first compressor specifically for GML documents compression. GPress exploits the unique characteristics of GML documents to achieve good performance. Extensive experiments over real-world GML documents show that GPress evidently outperforms XMill (one of the best existing XML compressors) in compression ratio, while its compression efficiency is comparable to the existing XML compressors.