The goal of object detection is to determine the class and location of objects in an image. This paper proposes a novel anchor-free, two-stage framework which first extracts a number of object proposals by finding potential corner keypoint combinations and then assigns a class label to each proposal by a standalone classification stage. We demonstrate that these two stages are effective solutions for improving recall and precision, respectively, and they can be integrated into an end-to-end network. Our approach, dubbed Corner Proposal Network (CPN), enjoys the ability to detect objects of various scales and also avoids being confused by a large number of false-positive proposals. On the MS-COCO dataset, CPN achieves an AP of 49.2% which is competitive among state-of-the-art object detection methods. CPN also fits the scenario of computational efficiency, which achieves an AP of 41.6%/39.7% at 26.2/43.3 FPS, surpassing most competitors with the same inference speed. Code is available at https://github.com/Duankaiwen/CPNDet