Keypoint-based detectors have achieved pretty-well performance. However, incorrect keypoint matching is still widespread and greatly affects the performance of the detector. In this paper, we propose CentripetalNet which uses centripetal shift to pair corner keypoints from the same instance. CentripetalNet predicts the position and the centripetal shift of the corner points and matches corners whose shifted results are aligned. Combining position information, our approach matches corner points more accurately than the conventional embedding approaches do. Corner pooling extracts information inside the bounding boxes onto the border. To make this information more aware at the corners, we design a cross-star deformable convolution network to conduct feature adaption. Furthermore, we explore instance segmentation on anchor-free detectors by equipping our CentripetalNet with a mask prediction module. On COCO test-dev, our CentripetalNet not only outperforms all existing anchor-free detectors with an AP of 48.0% but also achieves comparable performance to the state-of-the-art instance segmentation approaches with a 40.2% Mask AP. Code is available at https: //github.com/KiveeDong/CentripetalNet.