Three-dimensional (3D) object detection is an important task in the field of machine vision, in which the detection of 3D objects using monocular vision is even more challenging. We observe that most of the existing monocular methods focus on the design of the feature extraction framework or embedded geometric constraints, but ignore the possible errors in the intermediate process of the detection pipeline. These errors may be further amplified in the subsequent processes. After exploring the existing detection framework of keypoints, we find that the accuracy of keypoints prediction will seriously affect the solution of 3D object position. Therefore, we propose a novel keypoints uncertainty prediction network (KUP-Net) for monocular 3D object detection. In this work, we design an uncertainty prediction module to characterize the uncertainty that exists in keypoint prediction. Then, the uncertainty is used for joint optimization with object position. In addition, we adopt position-encoding to assist the uncertainty prediction, and use a timing coefficient to optimize the learning process. The experiments on our detector are conducted on the KI TTI benchmark. For the two levels of easy and moderate, we achieve accuracy of 17.26 and 11.78 in AP3D, and achieve accuracy of 23.59 and 16.63 in APBEV, which are higher than the latest method KM3D.