Automatic extraction of buildings in remote sensing images is an important but challenging task and finds many applications in different fields such as urban planning, navigation and so on. This paper addresses the problem of buildings extraction in very high-spatial-resolution (VHSR) remote sensing (RS) images, whose spatial resolution is often up to half meters and provides rich information about buildings. Based on the observation that buildings in VHSR-RS images are always more distinguishable in geometry than in texture or spectral domain, this paper proposes a geometric building index (GBI) for accurate building extraction, by computing the geometric saliency from VHSR-RS images. More precisely, given an image, the geometric saliency is derived from a mid-level geometric representations based on meaningful junctions that can locally describe geometrical structures of images. The resulting GBI is finally measured by integrating the derived geometric saliency of buildings. Experiments on three public and commonly used datasets demonstrate that the proposed GBI achieves the state-of-the-art performance and shows impressive generalization capability. Additionally, GBI preserves both the exact position and accurate shape of single buildings compared to existing methods.