Anchor-free detection methods identify different objects by perceiving bounding box keypoints without predefined anchor boxes, which have attracted much attention due to their straightforward design and comparable performance. Currently, most anchor-free methods detect bounding box corners to regress object locations. In clutter environments, the bounding box corners may lie in background regions, which have limited relation with the object itself. In addition, the relationships between object keypoints are always neglected, potentially affecting the perceptibility of the detector for high-precision object detection. In this paper, we propose the Keypoint Relational Regression Network (KRRNet) to detect object keypoints with semantic relations instead of bounding box corners. The relational regression head is designed to enhance the keypoint relationship exploration capability and reason accuracy object locations. Moreover, the random background sampling strategy is proposed to sample negative background points around foreground object regions and form point pairs with object keypoints. Then, KRRNet can explicitly learn discriminative feature embedding from contrastive learning to pull close the positive pairs and push apart the negative pairs, resisting the influence of surrounding complex environments. KRRNet can be trained on one Nvidia RTX 3090 GPU and achieves a single-scale test AP of 48.9% and multi-scale test AP of 50.6% on the MS-COCO test-dev with the backbone of Hourglass-104, surpassing state-of-the-art bottom-up anchor-free detector using the same backbone.