Gradient ghost imaging (GGI) is a new imaging method that can directly extract the edge of a target from the correlation of light intensity fluctuations. However, there are problems of poor image quality and practicability in GGI. The corner point is an important target feature and has important applications in the fields of image processing and machine vision. In this paper, we propose a corner detection scheme that combines a corner detection algorithm based on curvature scale space with a GGI system, which can directly extract corner points from the reconstruction results of ghost imaging. A simulation and experimental results show that our method can acquire precise and robust corner information of an unknown target in undersampled cases, which promotes the practical development of ghost imaging.